Circuit for displaying any Poincare section plane in three-dimensional space by using oscillograph

Abstract

The invention provides a circuit for displaying any Poincare section plane in a three-dimensional space by using an oscillograph, which comprises an input circuit, an any section plane generation circuit, a control signal forming circuit and a display signal forming circuit, wherein the input circuit is connected with the any section plane generation circuit which is connected with the control signal forming circuit; the control signal forming circuit is connected with the display signal forming circuit; and the input circuit is also connected with the display signal forming circuit. The invention provides a circuit for displaying the any Poincare section plane of a nonlinear system in the three-dimensional space. The circuit can be used for conveniently adjusting the direction and the position of the section plane on line at any time, thereby increasing the functions for the oscillograph of observing a motion curve internal structure of the nonlinear system and judging the stability of the system on line and providing a convenient and effective tool for detecting and recognizing the chaos state and chaos teaching demonstration and the like. The circuit disclosed by the invention can be used for flexibly adjusting the definition of the Poincare section plane and the intersecting points.

Description

(1) Technical field

[0001] The invention relates to electronic measurement technology, specifically an oscilloscope display circuit for an arbitrary Poincaré section plane in three-dimensional space. (2) Background technology

[0002] The Poincaré section is an effective method for studying nonlinear dynamical systems. It converts the continuous orbit of the dynamical system over time into the intersection point (discrete mapping) of the trajectory and a section (Poincaré section). While reducing the N-dimensional phase space to N-1-dimensional, the Poincaré section maintains the topology of the original continuous dynamical system. It is particularly convenient to judge the stability of a complex system with the Poincaré section. When the motion state of the system is periodic, there is only one fixed point or a few discrete fixed points on the Poincaré cross section; when the motion state of the system is quasi-periodic, the Poincaré cross section is a closed curve; when...

Examples

Embodiment 1

[0023] Example 1: Combining Figure 1-Figure 5 , the present invention a kind of oscilloscope display circuit of arbitrary Poincaré sectional plane in three-dimensional space, it is by input circuit (1), arbitrary sectional plane generating circuit (2), control signal forming circuit (3) and display signal forming circuit (4 ), the input circuit

[0024] (1) connect any sectional plane generating circuit (2), any sectional plane generating circuit (2) connect control signal forming circuit (3), control signal forming circuit (3) connect display signal forming circuit (4), input circuit (1 ) is also connected with the display signal forming circuit (4).

[0025] The present invention also has the following technical characteristics:

[0026] The arbitrary sectional plane generating circuit (2) includes resistances: R, R x1 , R x2 , R y1 , R y2 , R z1 , R z2 , R f1, R f2 , Potentiometer R P1 , the first double potentiometer (R Px ), the second double potentiometer (R...

Embodiment 2

[0029] Example 2: Combining Figure 1-Figure 11 , each circuit part of the present invention is introduced below:

[0030] 1. Input circuit

[0031] The purpose of the input circuit 1(1) is to realize the measurement of various system signals under test with an oscilloscope. The main function is to transform the impedance and scale up or down the signal as needed. Receive the voltage signal V of the three variables of the system under test x , V y and V z , output the corresponding three voltage signals V x ', V y ' and V z '.

[0032] 2. Arbitrary sectional plane generation circuit

[0033] Arbitrary sectional plane generation circuit 1 (2) is the generation circuit of any Poincaré section ax+by+cz=d (wherein a, b, c and d are arbitrary real values), such as figure 2 and Figure 5 shown. The dotted line frame part of the circuit is used to determine the direction of the input signal; the arbitrary section circuit is composed of an addition and subtraction hybrid ...

Embodiment 3

[0042] Example 3: Binding Figure 2-Figure 4 ,Figure 6- Figure 11 , the arbitrary sectional plane generating circuit (2) of the present invention, such as figure 2 shown. due to R f1 =R f2 =R f , R x1 =R x2 =R x , R y1 =R y2 =R y , R z1 =R z2 =R z , R Px1-1 =R Px1-2 =R Px , R Py1-1 =R Py1-2 =R Py , R Pz1-1 =R Pz1-2 =R Pz , and the 1 and 1' terminals are always connected to V x 'The other is grounded; 2 and 2' are always connected to V y 'The other is grounded; 3 and 3' are always connected to V z ’ Another ground. No matter how to adjust the double potentiometer R Px , R Py or R Pz , both guarantee that the op amp A 1 The resistance of the two input terminals is equal, that is, R f1 / / (R x1 +R Px1-1 ) / / (R y1 +R Py1-1 ) / / (R z1 +R Pz1-1 ) = R f2 / / (R x2 +R Px1-2 ) / / (R y2 +R Py1-2 ) / / (R z2 +R Pz1-2 ) = R f / / (R x1 +R Px ) / / (R y1 +R Py ) / / (R z1 +R Pz ). And because terminals 1, 2, and 3 are located in the operational amplifier (...

(1) Technical field

[0001] The invention relates to electronic measurement technology, specifically an oscilloscope display circuit for an arbitrary Poincaré section plane in three-dimensional space. (2) Background technology

[0002] The Poincaré section is an effective method for studying nonlinear dynamical systems. It converts the continuous orbit of the dynamical system over time into the intersection point (discrete mapping) of the trajectory and a section (Poincaré section). While reducing the N-dimensional phase space to N-1-dimensional, the Poincaré section maintains the topology of the original continuous dynamical system. It is particularly convenient to judge the stability of a complex system with the Poincaré section. When the motion state of the system is periodic, there is only one fixed point or a few discrete fixed points on the Poincaré cross section; when the motion state of the system is quasi-periodic, the Poincaré cross section is a closed curve; when...

Examples

Embodiment 1

[0023] Example 1: Combining Figure 1-Figure 5 , the present invention a kind of oscilloscope display circuit of arbitrary Poincaré sectional plane in three-dimensional space, it is by input circuit (1), arbitrary sectional plane generating circuit (2), control signal forming circuit (3) and display signal forming circuit (4 ), the input circuit

[0024] (1) connect any sectional plane generating circuit (2), any sectional plane generating circuit (2) connect control signal forming circuit (3), control signal forming circuit (3) connect display signal forming circuit (4), input circuit (1 ) is also connected with the display signal forming circuit (4).

[0025] The present invention also has the following technical characteristics:

[0026] The arbitrary sectional plane generating circuit (2) includes resistances: R, R x1 , R x2 , R y1 , R y2 , R z1 , R z2 , R f1, R f2 , Potentiometer R P1 , the first double potentiometer (R Px ), the second double potentiometer (R...

Embodiment 2

[0029] Example 2: Combining Figure 1-Figure 11 , each circuit part of the present invention is introduced below:

[0030] 1. Input circuit

[0031] The purpose of the input circuit 1(1) is to realize the measurement of various system signals under test with an oscilloscope. The main function is to transform the impedance and scale up or down the signal as needed. Receive the voltage signal V of the three variables of the system under test x , V y and V z , output the corresponding three voltage signals V x ', V y ' and V z '.

[0032] 2. Arbitrary sectional plane generation circuit

[0033] Arbitrary sectional plane generation circuit 1 (2) is the generation circuit of any Poincaré section ax+by+cz=d (wherein a, b, c and d are arbitrary real values), such as figure 2 and Figure 5 shown. The dotted line frame part of the circuit is used to determine the direction of the input signal; the arbitrary section circuit is composed of an addition and subtraction hybrid ...

Embodiment 3

[0042] Example 3: Binding Figure 2-Figure 4 ,Figure 6- Figure 11 , the arbitrary sectional plane generating circuit (2) of the present invention, such as figure 2 shown. due to R f1 =R f2 =R f , R x1 =R x2 =R x , R y1 =R y2 =R y , R z1 =R z2 =R z , R Px1-1 =R Px1-2 =R Px , R Py1-1 =R Py1-2 =R Py , R Pz1-1 =R Pz1-2 =R Pz , and the 1 and 1' terminals are always connected to V x 'The other is grounded; 2 and 2' are always connected to V y 'The other is grounded; 3 and 3' are always connected to V z ’ Another ground. No matter how to adjust the double potentiometer R Px , R Py or R Pz , both guarantee that the op amp A 1 The resistance of the two input terminals is equal, that is, R f1 / / (R x1 +R Px1-1 ) / / (R y1 +R Py1-1 ) / / (R z1 +R Pz1-1 ) = R f2 / / (R x2 +R Px1-2 ) / / (R y2 +R Py1-2 ) / / (R z2 +R Pz1-2 ) = R f / / (R x1 +R Px ) / / (R y1 +R Py ) / / (R z1 +R Pz ). And because terminals 1, 2, and 3 are located in the operational amplifier (...

Images