Design And Research Of New Multi-torus Memristive Chaotic System

As a new basic element of the circuit,memristor has wide application prospects in various fields such as computer storage system and neural network control due to its nonlinear characteristics and unique memory function.Memristors,due to their unique non-linear characteristics,can generate various types of chaotic signals with complex and variable dynamic characteristics when applied to the design of memristive chaotic systems.These types of chaotic signals are used in the fields of secure communication and synchronization control of chaos.It has very important research value,so it is of great significance to design a novel memristive chaotic system with rich chaotic characteristics.This paper designs a variety of new memristive multi-toroidal chaotic systems on the basis of various multi-toroidal chaotic systems.By constructing a new memristor model and using two memristor models in the same system,it is designed to contain multiple memristors.The novel memristor chaotic system of the resistor,and the numerical calculation of the system and the corresponding circuit simulation are realized.The specific work and innovation points of this paper are as follows:(1)On the basis of the third-order multifolded toroidal chaotic system,the experimentally verified memristor model is used to replace the resistors at different positions in the system circuit,and a variety of novel memristor chaotic systems are designed,and new transformations are obtained.The system state equation is used to compare and analyze the chaotic characteristics of the new system generated by each replacement form.The various chaotic characteristics of the system are obtained through simulation to verify the rich dynamic characteristics of the system,and the parameters of the system are adjusted to observe the chaotic phenomenon.Variety.Finally,according to the designed new memristive chaotic system,the circuit schematic is drawn,and the chaotic characteristics of the system are verified by simulation on the circuit simulation platform.(2)Based on the fourth-order multi-toroidal chaotic system,a smooth cubic function model and a smooth quadratic function model are selected and put into the system,and a memristor multi-toroid chaotic system including up to four memristors is designed.To obtain the system state equations under various transformations,to compare and analyze the chaotic characteristics of the new system generated in each case,to numerically calculate the system through MATLAB simulation,to obtain images of various chaotic characteristics of the system to verify the richness of the system.According to the dynamic characteristics of the system,the parameters of the system can be adjusted to observe the changes of chaotic phenomena,and the number of toruses with controllable torus can be obtained.The simulation can obtain two to eight chaotic systems with different numbers of torus.(3)Based on the fourth-order multi-directionally distributed grid multi-toroidal chaotic system,a mathematical model of the memristor is used to appropriately transform the system state equation,and a two-way distributed memristive multi-toroidal surface based on the memristor is designed.Chaotic system,three-dimensional distributed grid memristive multi-toroidal chaotic system,and four-directional distributed memristive multi-toroidal chaotic system,numerically calculate the various chaotic characteristics of the new system and implement hardware circuit design to adjust the system parameters to observe the changes in the chaos phenomenon.Finally,according to the designed new memristive chaotic system,the circuit schematic is drawn,and the chaotic characteristics of the system are verified by simulation on the circuit simulation platform.The experimental results of hardware design are consistent with the theoretical analysis results.The correctness of the design of a multidirectional distributed grid memristive multi-toroidal chaotic system is illustrated.