An optimal control method for malware propagation in heterogeneous networks of smart ships

Abstract

The present invention discloses an optimal control method for malware propagation in a heterogeneous network of a smart ship, comprising the following steps: constructing a network state node graph; obtaining a corresponding heterogeneous differential equation expression; establishing a cost function of an optimization target; defining co-state variables; and solving the control result corresponding to the differential equation. The smart ship heterogeneous network model proposed by the present invention considers a heterogeneous model of a surface and underwater wireless sensor network combined with a time-delay state, simulates the transformation of node states in the network by constructing relevant differential equations, analyzes and studies the diffusion state of malware in the smart ship network, and solves the control parameters of the optimal cost. The node states in the network are divided into four states: generally susceptible, generally infected by malware, low-energy susceptible, and low-energy infected by malware. According to the method of treating and controlling malware in the network, while considering the cost of controlling and treating, an objective function that minimizes the optimization cost is constructed.

Description

Technical Field

[0001] The present invention relates to the technical field of smart ships, and in particular to an optimal control method for the propagation of malware in a heterogeneous network of a smart ship. Background Art

[0002] Underwater wireless sensor networks (UWSNs) based on wireless sensor networks (WSNs) have received attention in recent years. As a sensor network communication technology applied to the inside of water bodies, it is widely used in the collection and monitoring of information in smart ships, such as the exploration of marine resources, the detection of environmental pollution, the navigation system of waterways, and underwater hazard warnings. UWSNs are mainly composed of corrosion-resistant sensor node networks that can work underwater, surface information collection base stations, and waterway communication vessels. UWSNs nodes can adapt to the complex underwater working environment with the convenience of self-organizing networks. However, unlike traditional WSNs on land, UWSNs network nodes face challenges such as limited power and difficulty in laying underwater charging cables. Therefore, the application of wireless power transmission technology (WPT) is UWSNs. A feasible solution to maintain normal network functions in the underwater environment. Due to the particularity of the underwater working environment, the traditional optical communication has serious signal attenuation in the water and can only adapt to some short-distance data collection and transmission, and its applicability is not high. Therefore, based on cost considerations, underwater networks mostly use underwater acoustic network communications suitable for long-distance communications. Underwater acoustic network communications mainly involve underwater network nodes with different functions collecting data and transmitting information through an underwater acoustic multi-hop network. After the data is gathered at the cluster head node, the surface base station collects and processes the information and transmits it to the shipping vessel via radio, or the shipping vessel directly communicates with the network information transceiver node. Although underwater acoustic communication has a small sound wave attenuation and can achieve communication transmission over several kilometers, it also faces huge challenges due to its characteristics such as extended propagation time, serious multipath effect, and limited communication bandwidth.

[0003] Due to its open information transmission and reception method, wireless sensor networks are more vulnerable to malware attacks than traditional wired networks. Malware refers to programs that have the ability to exploit target system vulnerabilities to invade and penetrate the system, and replicate themselves to infect other system members. The penetration of malware can have serious impacts on the system, including information leakage, extortion, system energy exhaustion, and functional paralysis. Based on the particularity of scale-free networks, the propagation characteristics of malware in sensor networks can be simulated using infectious disease models. At the same time, due to the special working environment and transmission technology of UWSNs, the study of underwater wireless sensor networks needs to consider more the time lag effect of underwater acoustic transmission and the charging and discharging state of underwater limited energy nodes. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the shortcomings of the prior art, the present invention provides an optimal control method for malware propagation in a heterogeneous network of a smart ship, which has the advantages of considering the cost of control treatment and constructing an objective function that minimizes the optimization cost, so as to solve the problem that wireless sensor networks are more vulnerable to malware attacks than traditional wired networks due to their open information transmission and reception methods.

[0006] (II) Technical solution

[0007] In order to achieve the above-mentioned consideration of controlling the cost of treatment and constructing an objective function for minimizing the optimization cost, the present invention provides the following technical solutions:

[0008] An optimal control method for malware propagation in a smart ship heterogeneous network comprises the following steps:

[0009] S1. Build a network status node graph

[0010] The network nodes in the scale-free network of smart ship sensors are divided into n subgroups, which represent node subgroups of different degrees. The subgroups satisfy the following relationship: 1 = N1 + N2 + N3 + ... + N n , 1≤k≤n, where N k It represents the ratio of the sum of nodes with node degree k to the total number of nodes, so 0≤N k <1, and N k =S k (t)+L k (t)+LS k (t)+LI k (t), where for S k (t) represents the proportion of susceptible nodes to all nodes in the node subgroup with node degree k. Due to the vulnerability of wireless networks, susceptible nodes are easily attacked and infected by infected nodes, and are transformed into infected nodes to further spread the infection. k (t-τ)Θ(t-τ), α1kS k (t-τ)Θ(t-τ) definition: in represents the average degree of the network, and p(h) represents the frequency of nodes with degree h in the network, so kp(j|k)I j (t-τ) represents a susceptible node S with degree k k (t) Successfully connected to the infected node I with node degree j j (t-τ); considering that the laying distance between underwater nodes is generally long and underwater acoustic communication has a delay characteristic, it is assumed here that there is an average delay τ in the communication between underwater nodes.

[0011] S2. Obtain the corresponding heterogeneous differential equation expression

[0012] Based on the above explanation of the node definition and function, the following differential expressions are listed according to the graph:

[0013]

[0014] S3. Establishing the cost function of the optimization target

[0015] According to the Pondriagin maximum principle, the present invention introduces a malware control scheme based on the optimization of treatment cost, which is reflected in the optimization of β k With γ k Therefore, the differential expression is changed to:

[0016]

[0017] The following objective function is established by weighing the cost and control effect, and the relevant Hamiltonian function is set up to minimize the objective function:

[0018]

[0019] A k , B k , are the cost coefficients for treating infected nodes and low-energy infected nodes,

[0020] The Lagrangian function is:

[0021]

[0022] S4. Define co-state variables

[0023] set up

[0024] x=(S k (t), I k (t), LS k (t), LI k (t)) T , x τ =(S k (t-τ), I k (t-τ), LS k (t-τ), LI k (t-τ) T ,

[0025] λ=(λ 1k (t), λ 2k (t), λ 3k (t), λ 4k (t)) T

[0026] x=(S k (t), I k (t), LS k (t), LI k (t)) T , x τ =(S k (t-τ), I k (t-τ), LS k (t-τ), LI k (t-τ))T,

[0027] λ=(λ 1k (t), λ 2k (t), λ 3k (t), λ 4k (t)) T

[0028] According to the cost function, construct the Hamiltonian function:

[0029]

[0030] where λ ik (t)(i=1,2,3,4) is defined as the corresponding S k (t), I k (t), LS k (t), LI k (t) is the covariate of the

[0031] S5. Solve the differential equation and obtain the control result

[0032] The co-state variables established in step S4 need to satisfy the following three equations:

[0033] Equation of state: (where H λ is the partial derivative of H with respect to λ); optimization conditions: (where H i is the partial derivative of H with respect to i, i = β, γ), then:

[0034] Co-state

[0035] Differential equations of variables:

[0036]

[0037] The covariate differential equation is as follows:

[0038]

[0039] From the optimization objective function, we can know that there is no corresponding optimization target for the state variable x(t) at the last control moment tf, so the cross-sectional condition is λ i (tf)=0, (i=1, 2, 3, 4);

[0040] Finally, the optimal control treatment plan is obtained by the above co-variables and optimization conditions:

[0041]

[0042]

[0043] Preferably, in step S1, for I k (t): the proportion of infected nodes to the total number of nodes in the node subgroup with node degree k, which has the ability to infect other susceptible nodes;

[0044] For I k (t) Definition in the state transition diagram: Same as above, assuming that the damage rate and power of infected nodes and susceptible nodes are the same, so I k (t) at a rate b k I k The rate of migration out of the network and μ 1k I k (t) is converted to the low-energy infected node LI k (t), due to human efforts to remove malware from smart ship sensor networks, I k (t) at a rate of β k I k (t) is transformed into a susceptible node S k (t).

[0045] Preferably, in step S1, LS k (t): The proportion of low-energy susceptible nodes to all nodes in the node subgroup with node degree k. Due to the lack of operating energy, the node cannot communicate normally with other nodes in the network;

[0046] For LS k (t) Definition of the state transition diagram: Same as above, assuming that the damage rate of low-energy susceptible nodes is the same as that of susceptible nodes, so LS k (t) at a rate b k LS k The rate of migration out of the network, at the same time, due to the wireless charging of the network underwater, LS k (t) μ 2k LS k (t) is converted to the susceptible node S k (t).

[0047] Preferably, in step S1, LIk (t): The proportion of low-energy infected nodes to the total number of nodes in the node subgroup with node degree k. Due to the lack of operating energy, the node cannot communicate normally with other nodes in the network;

[0048] For LI k (t) Definition of the state transition diagram: Same as above, assuming that the damage rate of low-energy infected nodes is the same as that of susceptible nodes, so LI k (t) at a rate b k LI k The rate of migration out of the network, at the same time, due to the wireless charging of the network underwater, LI k (t) μ 2k LI k The rate of (t) is converted to the infected node I k (t). And because charging can also remove malware from low-energy infected nodes, LI k (t) at a rate γ k LI k (t) is transformed into a susceptible node S k (t).

[0049] Preferably, in step S1: D k (t) represents a dead node, which usually describes a node that has migrated out of the underwater network. It cannot communicate with any underwater node and cannot play any role in the underwater network.

[0050] Preferably, in step S1: for α2S k (t), we assume that in the smart ship sensor network, the communication link between the surface ship and the underwater node is one-to-one communication, so α2 is the number of times the surface ship carrying malware successfully infects the underwater susceptible node S k The probability of (t) is independent of the degree of the nodes in the underwater scale-free network, but only depends on whether the ship successfully establishes a pair of communications with the underwater network.

[0051] Preferably, in step S1: for S k (t) In the definition of the state transition diagram: Since the life span of the node is limited, the node is b k S k The rate of migration out of the system network, b k is the node damage rate. In order to maintain the constant number of system nodes, the rate b k New nodes are constantly introduced into the system; and since the nodes have limited power, S k (t) with probability μ 1k S k (t) Transformed to low energy susceptible node LS k (t); there is α1kS per unit timek (t-τ)Θ(t-τ)+α2S k (t) Node ratio S k (t) for infected node I k (t) conversion.

[0052] Preferably, in step S1: α1 is the infection rate, which means the number of susceptible nodes S in a unit time. k (t) and infected node I k (t) The probability of successfully establishing communication and replicating malware so that a susceptible node becomes an infected node, therefore, α1kS k (t-τ)Θ(t-τ) represents the network S per unit time k (t) Infected and transformed into I k The probability of (t).

[0053] (III) Beneficial effects

[0054] Compared with the prior art, the optimal control method for malware propagation in a smart ship heterogeneous network provided by the present invention has the following beneficial effects:

[0055] 1. The optimal control method for malware propagation in the heterogeneous network of smart ships. Through actual application scenarios, a heterogeneous model of surface and underwater wireless sensor networks combined with time-delay states is constructed. The diffusion properties of malware in smart ship networks are analyzed and studied. The transformation of node states in the network is simulated by constructing relevant differential equations, which are mainly divided into four types: general susceptible state of nodes, general infected state by malware, low-energy susceptible state, and low-energy infected state. According to the treatment methods for malware in the network, while considering the cost of controlling treatment, an objective function that minimizes the optimization cost is constructed.

[0056] 2. The optimal control method for malware propagation in the heterogeneous network of the smart ship, through the application of the Pondriagin maximum principle, constructs the co-state equation corresponding to the Hamiltonian function of the model and the objective function. List the optimization conditions and obtain the optimal treatment cost control scheme through iterative solution. Based on the SIS (susceptible-infected-susceptible) infectious disease model, the present invention expands the modeling of low-energy states and time-lag effects of underwater acoustic propagation in the scene, proposes the SISL (susceptible-infected-susceptible-low energy) model, and considers the node degree of the network according to the differences in network topology and extends it to the modeling and analysis of heterogeneous networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic diagram of network node status of an optimal control method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] Example:

[0060] See also Figure 1 The optimal control method for malware propagation in a smart ship heterogeneous network provided by an embodiment of the present invention comprises the following steps:

[0061] S1. Build network status node graph

[0062] The network nodes in the scale-free network of smart ship sensors are divided into n subgroups, which represent node subgroups of different degrees. The subgroups satisfy the following relationship: 1 = N1 + N2 + N3 + ... + N n , 1≤k≤n, where N k It represents the ratio of the sum of nodes with node degree k to the total number of nodes, so 0≤N k <1, and N k =S k (t)+L k (t)+LS k (t)+LI k (t), where for S k (t) represents the proportion of susceptible nodes to all nodes in the node subgroup with node degree k. Due to the vulnerability of wireless networks, susceptible nodes are easily attacked and infected by infected nodes, and are transformed into infected nodes to further spread the infection. k (t-τ)Θ(t-τ), α1kS k (t-τ)Θ(t-τ) definition: in represents the average degree of the network, and p(h) represents the frequency of nodes with degree h in the network, so kp(j|k)I j (t-τ) represents a susceptible node S with degree k k (t) Successfully connected to the infected node I with node degree j j (t-τ); Considering that the laying distance between underwater nodes is generally long, underwater acoustic communication has a delay characteristic. Here, it is assumed that there is an average delay τ between underwater nodes. k (t): The proportion of infected nodes to the total number of nodes in the node subgroup with node degree k, which has the ability to infect other susceptible nodes. k(t) Definition in the state transition diagram: Same as above, assuming that the damage rate and power of infected nodes and susceptible nodes are the same, so I k (t) at a rate b k I k The rate of migration out of the network and μ 1k I k (t) is converted to the low-energy infected node LI k (t), due to human efforts to remove malware from smart ship sensor networks, I k (t) at a rate of β k I k (t) is transformed into a susceptible node S k (t), for LS k (t): The proportion of low-energy susceptible nodes to all nodes in the node subgroup with node degree k. Due to the lack of operating energy, the node cannot communicate normally with other nodes in the network; for LS k (t) Definition of the state transition diagram: Same as above, assuming that the damage rate of low-energy susceptible nodes is the same as that of susceptible nodes, so LS k (t) at a rate b k LS k The rate of migration out of the network, at the same time, due to the wireless charging of the network underwater, LS k (t) μ 2k LS k (t) is converted to the susceptible node S k (t), for LI k (t): The proportion of low-energy infected nodes to the total number of nodes in the node subgroup with node degree k. Due to the lack of operating energy, the node cannot communicate normally with other nodes in the network. k (t) Definition of the state transition diagram: Same as above, assuming that the damage rate of low-energy infected nodes is the same as that of susceptible nodes, so LI k (t) at a rate b k LI k The rate of migration out of the network, at the same time, due to the wireless charging of the network underwater, LI k (t) μ 2k LI k The rate of (t) is converted to the infected node I k (t). And because charging can also remove malware from low-energy infected nodes, LI k (t) at a rate γ k LI k (t) is transformed into a susceptible node S k (t), where D k(t) represents a dead node, which usually describes a node that has migrated out of the underwater network. It cannot communicate with any underwater node and cannot play any role in the underwater network. For α2S k (t), we assume that in the smart ship sensor network, the communication link between the surface ship and the underwater node is one-to-one communication, so α2 is the number of times the surface ship carrying malware successfully infects the underwater susceptible node S k The probability of (t) is independent of the degree of the nodes in the underwater scale-free network, and is only related to whether the ship successfully establishes a pair of communications with the underwater network. k (t) In the definition of the state transition diagram: Since the life span of the node is limited, the node is b k S k The rate of migration out of the system network, b k is the node damage rate. In order to maintain the constant number of system nodes, the rate b k New nodes are constantly introduced into the system; and since the nodes have limited power, S k (t) with probability μ 1k S k (t) Transformed to low energy susceptible node LS k (t); there is α1kS per unit time k (t-τ)Θ(t-τ)+α2S k (t) Node ratio S k (t) for infected node I k (t), α1 is the infection rate, which means the number of susceptible nodes S per unit time. k (t) and infected node I k (t) The probability of successfully establishing communication and replicating malware so that a susceptible node becomes an infected node, therefore, α1kS k (t-τ)Θ(t-τ) represents the network S per unit time k (t) Infected and transformed into I k The probability of (t).

[0063] S2. Obtain the corresponding heterogeneous differential equation expression

[0064] Based on the above explanation of the node definition and function, the following differential expressions are listed according to the graph:

[0065]

[0066] S3. Establishing the cost function of the optimization target

[0067] According to the Pondriagin maximum principle, the present invention introduces a malware control scheme based on the optimization of treatment cost, which is reflected in the optimization of β k With γ kTherefore, the differential expression is changed to:

[0068]

[0069] The following objective function is established by weighing the cost and control effect, and the relevant Hamiltonian function is set up to minimize the objective function:

[0070]

[0071] A k , B k , are the cost coefficients for treating infected nodes and low-energy infected nodes,

[0072] The Lagrangian function is:

[0073]

[0074] S4. Define co-state variables

[0075] set up

[0076] x=(S k (t), I k (t), LS k (t), LI k (t)) T , x τ =(S k (t-τ), I k (t-τ), LS k (t-τ), LI k (t-τ) T ,

[0077] λ=(λ 1k (t), λ 2k (t), λ 3k (t), λ 4k (t)) T

[0078] x=(S k (t), I k (t), LS k (t), LI k (t)) T , x τ =(S k (t-τ), I k (t-τ), LS k (t-τ), LI k (t-τ) T ,

[0079] λ=(λ 1k(t), λ 2k (t), λ 3k (t), λ 4k (t)) T

[0080] According to the cost function, construct the Hamiltonian function:

[0081]

[0082] where λ ik (t)(i=1,2,3,4) is defined as the corresponding S k (t), I k (t), LS k (t), LI k (t) is the covariate of the

[0083] S5. Solve the differential equation and obtain the control result

[0084] The co-state variables established in step S4 need to satisfy the following three equations:

[0085] Equation of state: (where H λ is the partial derivative of H with respect to λ); optimization conditions: (where H i is the partial derivative of H with respect to i, i = β, γ), then:

[0086] Covariate differential equations:

[0087]

[0088] The covariate differential equation is as follows:

[0089]

[0090] From the optimization objective function, we can know that there is no corresponding optimization target for the state variable x(t) at the last control moment tf, so the cross-sectional condition is λ i (tf)=0, (i=1, 2, 3, 4);

[0091] Finally, the optimal control treatment plan is obtained by the above co-variables and optimization conditions:

[0092]

[0093]

[0094] The above embodiment of the present invention proposes a new intelligent ship heterogeneous network model, considers the heterogeneous model of the surface and underwater wireless sensor network combined with the time-delay state, simulates the transformation of the node state in the network by constructing relevant differential equations, analyzes and studies the diffusion state of malware in the intelligent ship network, and solves the control parameters of the optimal cost. The node states in the network are divided into four types: general susceptible state, general malware infected state, low energy susceptible state, and low energy malware infected state. According to the method of malware treatment control in the network, while considering the cost of control treatment, an objective function that minimizes the optimization cost is constructed.

[0095] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An optimal control method for malware propagation in a smart ship heterogeneous network, characterized in that: The following steps are involved: S1. Build a network status node graph The network nodes in the scale-free network of smart ship sensors are divided into n subgroups, which represent node subgroups of different degrees. The subgroups satisfy the following relationship: ,in Represents the node degree as The sum of the nodes accounts for the proportion of the total number of nodes, so there is ,and ,in, , , are the corresponding proportions of infected nodes with node degree k, low-energy susceptible nodes, and low-energy infected nodes. , represents the proportion of susceptible nodes to all nodes in the node subgroup with node degree k. Due to the vulnerability of wireless networks, susceptible nodes are easily attacked and infected by infected nodes, and transformed into infected nodes to further spread the infection. The parameter t represents the size of each quantity at a certain time t, which represents time. middle, definition: ,in, is the infection rate of the infected node, , represents the average degree of the network, and p(j) represents the frequency of nodes with degree j appearing in the network, so Represents a susceptible node with degree k Successfully connected to an infected node with node degree j The probability of assuming that there is an average delay in the communication between underwater nodes ; S2. Obtain the corresponding heterogeneous differential equation expression Based on the above explanation of node definition and function, and according to the principle of transfer relationship, the following differential expressions are listed: ； S3. Establishing the cost function of the optimization target According to the Pondriagin maximum principle, a malware control scheme based on the optimization of treatment cost is introduced. and The optimization process is performed, so the differential expression is changed to: ； The following objective function is established by weighing the cost and control effect, and the relevant Hamiltonian function is set up to minimize the objective function: ； , , are the cost coefficients for treating infected nodes and low-energy infected nodes, The Lagrangian function is: ； S4. Define co-state variables set up ； According to the cost function, construct the Hamiltonian function: ； in Defined as corresponding covariates of ; S5. Solve the differential equation and obtain the control result The co-state variables established in step S4 need to satisfy the following three equations: Equation of state: ,in for right Partial derivatives of; Optimization conditions: , ,in for right The partial derivative of , then: , ; Covariate differential equations: ； The covariate differential equation is as follows: ; From the optimization objective function, we know that in controlling the final There is no corresponding state variable at the moment The optimization goal is, so the transversality condition is , ; Finally, the optimal control treatment plan is obtained by the above co-variables and optimization conditions: ； 。 2. The optimal control method for malware propagation in a smart ship heterogeneous network according to claim 1 is characterized in that: In step S1, for : The proportion of infected nodes to the total number of nodes in the node subgroup with node degree k, which has the ability to infect other susceptible nodes; for In the definition of the state transition diagram: Assume that the damage rate and power of the infected node and the susceptible node are the same, so At rate The rate of migration out of the network and The rate of conversion to low-energy infected nodes ,Due to the human removal of malware in smart ship sensor networks, At rate Transformed into susceptible nodes .

3. The optimal control method for malware propagation in a smart ship heterogeneous network according to claim 1 is characterized in that: In the step S1, : The proportion of low-energy susceptible nodes to all nodes in the node subgroup with node degree k. Due to the lack of operating energy, the node cannot communicate normally with other nodes in the network; for In the definition of the state transition diagram: Assume that the damage rate of low-energy susceptible nodes is the same as that of susceptible nodes, so At rate The network is migrated out of the network at a rate of 10000 Mbps. At the same time, the network is wirelessly charged underwater. by The rate of conversion to susceptible nodes .

4. The optimal control method for malware propagation in a smart ship heterogeneous network according to claim 1 is characterized in that: In the step S1, : The proportion of low-energy infected nodes to the total number of nodes in the node subgroup with node degree k. Due to the lack of operating energy, the node cannot communicate normally with other nodes in the network; for In the definition of the state transition graph: Assume that the low-energy infected nodes have the same damage rate as the susceptible nodes, so At rate The network is migrated out of the network at a rate of 10000 Mbps. At the same time, the network is wirelessly charged underwater. by The rate of conversion to infected nodes , and because charging can also clear malware from low-energy infected nodes, At rate Transformed into susceptible nodes .

5. The optimal control method for malware propagation in a smart ship heterogeneous network according to claim 1 is characterized in that: In step S1: Dead Node stands for Dead Node, which usually describes a node that has migrated out of an underwater network. It cannot communicate with any underwater node and cannot play any role in the underwater network.

6. The optimal control method for malware propagation in a smart ship heterogeneous network according to claim 1 is characterized in that: In step S1: ,We assume that in the smart ship sensor network, the communication link between the surface ship and the underwater node is one-to-one communication, so The surface ship carrying malware successfully infected the underwater susceptible node The probability of establishing a communication channel with the underwater network is independent of the degree of the nodes in the underwater scale-free network, but only depends on whether the ship successfully establishes a pair of communications with the underwater network.

7. The optimal method for malware propagation in a smart ship heterogeneous network according to claim 1 The control method is characterized in that In step S1: In the definition of the state transition diagram: Since the life span of the node is limited, the node is The rate of migration out of the system network, is the node damage rate. In order to maintain the constant number of system nodes, the rate New nodes are constantly introduced into the system; and because the nodes have limited power, By probability Transformed to low energy susceptible nodes ; Existence per unit time Node ratio Infected nodes conversion.

8. The optimal method for malware propagation in a smart ship heterogeneous network according to claim 1 The control method is characterized in that In the step S1: wherein, is the infection rate, which means the number of susceptible nodes per unit time Infected Nodes The probability of successfully establishing communication and replicating malware so that a susceptible node becomes an infected node, therefore, Indicates the unit time in the network Infected into probability.

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