Dynamic behavior analysis method based on small world network model

Abstract

The invention provides a dynamic behavior analysis method based on a small world network model. The invention discloses a fractional-order design method of the small world network model, and the method comprises a step of giving an integer-order small world network model of a controlled object and converting the original integer-order small world network model into a fractional-order small world network model through a fractional-order theory and method, a step of selecting a system delay parameter as a bifurcation parameter and carrying out stability and bifurcation analysis on a controlled system through a corresponding theory, and a step of obtaining corresponding conclusions through the analysis of a characteristic equation of the controlled system and finally verifying the correctnessof the theory and the characteristics of a dynamic behavior through MATLAB simulation. According to the method, the original integer-order model is in a transition to the fractional-order model for research, by selecting appropriate delay parameters and fractional-order exponents, the stability of the system is changed, and the increase or decrease of a stability domain can be controlled by specific parameter settings, and the controlled system has better operability.

Description

technical field [0001] The invention relates to an analysis method of fractional-order dynamic behavior based on a small-world network model, and belongs to the technical field of controllers. Background technique [0002] At present, in many fields, the small-world network is regarded as a type of mathematical graph. A characteristic of this type of graph is that most of the nodes in the graph are not adjacent to other nodes, but Most of the nodes can be reached from other points through a few steps. In addition, if the points in a small-world network are represented as a person, and the connecting lines are represented as mutual acquaintances, then this small-world network can show the small-world phenomenon that strangers are connected by people who know each other. In 1998, Watts and Strogatz proposed a small-world network model network, which was used to describe a gradual process from a regular network to a random network. The N-W model was also proposed in the same ...

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Problems solved by technology

The N-W model was also proposed in the same year, but it did not take into account the communication delay of the system

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