CN-117459204-B - Memristor-based chaotic synchronization system construction and FPGA circuit implementation method

CN117459204BCN 117459204 BCN117459204 BCN 117459204BCN-117459204-B

Abstract

The invention provides a memristor-based chaotic synchronization system construction and an FPGA circuit implementation method, which comprises the following steps of 1, constructing a memristor-based chaotic synchronization system; step 2, discretizing the memristor chaotic synchronous system to obtain a discretization equation, step 3, designing each module of the FPGA chaotic signal generator, converting the discretization equation into a hardware design language, step 4, designing based on a state machine, solving a chaotic sequence, and step 5, simulating and verifying a designed program in a board level, and analyzing the implementation effect. The chaotic synchronization system is added with the memristor, so that the chaotic synchronization system has more complex dynamic behavior and anti-noise performance, can reach a synchronous state more quickly, and can stably converge errors.

Inventors

ZUO CHAO
SONG JUNLEI
CHEN MENG
WANG ZUOSHUAI
WANG JIANXUN
XIAO HANCHEN
Geng pan
Dong kaifeng
ZHOU YOUYOU
JIN FANG

Assignees

中国船舶集团有限公司第七一九研究所
中国地质大学（武汉）

Dates

Publication Date: 20260505
Application Date: 20230808

Claims (3)

1. The method for constructing the memristor-based chaotic synchronization system and realizing the FPGA circuit is characterized by comprising the following steps of: step1, constructing a chaotic synchronization system based on a memristor; step 2, discretizing a chaos synchronous system based on a memristor to obtain a discretization equation; Step 3, designing each module of the FPGA chaotic signal generator, and converting a discretization equation into a hardware design language; Step 4, designing based on a state machine, and solving a chaotic sequence; Step 5, simulating and verifying the designed program at the board level, and analyzing the realization effect; In step 1, the method further comprises the following steps: step 11, adding a memristor into a Van der pol-Duffing chaotic system to obtain a mathematical model; Step 12, adding a controller to the mathematical model Obtaining a chaotic synchronization system model based on a memristor; Step 13, defining an error system, and converting the synchronization problem of the chaotic synchronization system based on the memristor into the stability problem of the error system; in step 11, the mathematical model and its differential equation are: ; ; Wherein x is The voltage is represented by a voltage value, Representing the non-linear damping coefficient of the device, Representing the amplitude of the sinusoidal signal, ω represents the angular frequency of the sinusoidal signal, and W (φ) represents the memristance of the memristor, which is represented by the magnetic flux φ, i.e A and b are constants, and the magnetic flux phi is equal to the integral of the voltages at two ends of the memristor with respect to time; is a state variable of a Van der pol-Duffing chaotic system added with a memristor; In step 12, a controller is added to the differential equation of the mathematical model The method comprises the following steps of: ; Wherein, the The state variable of the controller is the formula of the memristor-based chaotic synchronization system: ; Wherein, the For the controller, design the controller The method comprises the following steps: (5) Wherein, the Is a constant value, and is used for the treatment of the skin, Respectively represent ; In step 13, an error system is defined as The method comprises the following steps: ; the synchronization problem of the chaotic synchronization system based on the memristor is converted into the stability problem of the error system, and the controller is provided with the system Needs to meet the requirements of , 。
2. The method for constructing the memristor-based chaotic synchronization system and implementing the FPGA circuit according to claim 1, further comprising the following steps in step 2: step 21, constructing a vibrator model of a chaotic synchronization system based on a memristor; Selecting controller parameters: , The oscillator model of the memristor-based chaotic synchronization system can be expressed as: ; Step 22, discretizing a vibrator model of the chaotic synchronization system based on the memristor Discretizing a vibrator model of a chaotic synchronous system based on a memristor by using an improved Euler algorithm to obtain the following discretization equation: ; Wherein: ; ; Wherein, the Is the discrete value of the state variable at the current time, For the discrete value of the state variable at the next moment, h is the iteration step, Is a driving force signal.
3. The method for constructing the memristor-based chaotic synchronization system and realizing the FPGA circuit according to claim 2, wherein in the step 3, the FPGA chaotic signal generator comprises a DDS module, an Euler module and a DAC output module; The DDS module generates a driving force signal required by the system, decomposes the sinusoidal signal into 4096 equal parts, stores the equal parts into a ROM block of the FPGA, reads the address of the RAM, and provides the numerical value of the sinusoidal signal for the Euler module for operation; The Euler module calculates the input discrete signals to obtain state variable discrete values at the next time after iteration; And the DAC output module converts the chaos variable value obtained by calculation of the Euler module into an analog signal and transmits the analog signal to the oscilloscope for display.

Description

Memristor-based chaotic synchronization system construction and FPGA circuit implementation method Technical Field The invention relates to the technical field of analog circuits, in particular to a memristor-based chaotic synchronization system construction and FPGA circuit implementation method. Background Nonlinear science is a comprehensive discipline, the development of which is based on branches of various disciplines characterized by nonlinearity and the like, wherein the chaos theory is one of the most important parts in the nonlinear science, and has wide application prospects in the fields of secret communication systems, neural networks, artificial intelligence, load prediction, signal detection and the like, and has been paid more attention in recent years. The chaotic system shows sensitivity to initial conditions and complexity of chaotic signals, so that the chaotic system is widely applied to nonlinear science, information science, secret communication and other engineering fields. In the field of signal detection and processing, the nonlinear characteristic of the chaotic system can be used for improving the recognition and extraction of signals, and the chaotic signal processing technology can be applied to a communication system, a radar system and the like, so that the anti-interference capability and the information extraction effect of the signals are improved. The generation of the chaotic phenomenon mainly depends on a nonlinear device in a circuit system, the existing method for generating the chaotic signal is mainly realized by constructing basic operation circuits through discrete elements such as an operational amplifier, a capacitor, a resistor and the like and then connecting the basic operation circuits through a combination, the scheme has the defects that (1) the analog device is easily affected by temperature, voltage change and the like, component parameters can change along with the aging of the device, environmental factors can possibly generate certain electromagnetic interference and noise on the component, the numerical value of the component is changed, the experimental result is affected, and (2) each analog circuit cannot be reused after being constructed, and each circuit can only correspond to one chaotic circuit and has poor universality. Disclosure of Invention The invention provides a memristor-based chaotic synchronization system construction and FPGA circuit implementation method, which expands the state space and dynamic range of the chaotic system and ensures that the dynamic behavior of the system is richer and more complex. Specifically, the invention provides a memristor-based chaotic synchronization system construction and FPGA circuit implementation method, which comprises the following steps: Step 1, constructing a memristor chaotic synchronization system; step 2, discretizing the memristor chaotic synchronous system to obtain a discretization equation; Step 3, designing each module of the FPGA chaotic signal generator, and converting a discretization equation into a hardware design language; Step 4, designing based on a state machine, and solving a chaotic sequence; and 5, simulating and verifying the designed program at the board level, and analyzing the realization effect. Further, in step1, the method further comprises the steps of: step 11, adding a memristor into a Van der pol-Duffing chaotic system to obtain a mathematical model; Step 12, adding a controller u into the mathematical model to obtain a memristor-based chaotic synchronization system model; And step 13, defining an error system, and converting the synchronization problem of the synchronization system into the stability problem of the error system. Further, in step 11, the mathematical model and its differential equation are: where x (t) represents the voltage, α represents the nonlinear damping coefficient, F represents the amplitude of the sinusoidal signal, ω represents the angular frequency of the sinusoidal signal, Representing the memristance of a memristor, which is composed of magnetic fluxRepresentation, i.e.A. b are constants, magnetic fluxEqual to the integral of the voltage across the memristor over time, x 1、x2、x3 is the state variable of the system. Further, in step 12, a controller u is added to the differential equation of the mathematical model, resulting in: Wherein y 1、y2、y3 is a state variable of the system, and a formula of the memristor-based chaotic synchronization system is as follows: Wherein u is a controller, and the design controller u is: where u 1,u2,u3 is a constant and e 1,e2,e3 represents y 1-x1,y2-x2,y3-x3, respectively. Further, in step 13, an error system is defined as e=y-x, with: converting synchronization problem of synchronization system into stability problem of error system, the requirement for controller u is satisfied i=1,2,3,4。 Further, in step 2, the method further comprises the following steps: step 21, constructing a memristor chaotic