Modeling,Analysis And Circuit Implementation Of Multi-Scroll Chaotic Systems

How to generate multi-scroll chaotic attractors with more complex topology and apply them to encrypted communication has been widely concerned.The researches show that,compared with dissipative chaos,conservative chaos has better ergodicity and is more suitable for encryption.In recent years,it is found that multi-scroll chaotic dynamics also exists in some neuron models and circuit models,which is worthy of indepth study.Due to its synaptic plasticity,memristors can describe the effect of electromagnetic radiation on neurons,and can be used as the synapse weights of neural networks to help people better understand the neuro-dynamics characteristics.Furthermore,a multi-scroll chaotic system with complex dynamical behaviors can be conducted by utilizing the memristor with the natural nonlinearity.The following works focus on conservative multi-scroll chaotic systems and memristive multi-scroll chaotic systems,and the main contents are as follows.(1)A multi-directional controllable conservative multi-scroll chaotic system is constructed based on the generalized Hamiltonian system theory.The generation mechanism of chaos is explained through equilibrium analysis,and the conservative motion trajectory and bifurcation behavior of the system are analyzed by simulations.Furthermore,the pseudo-randomness test for conservative multi-scroll chaotic signals is performed.After that,the conservative multi-scroll chaotic sequences are captured based on FPGA platform.(2)A new locally active memristor is constructed,and a memristive FHN neuron model is proposed based on the memristor theory.By analyzing the dynamical effects of coupling strength and external stimuli,the multi-scroll dynamical characteristics can be observed.The switching mechanisms of discharge behaviors are explained by energy analysis,and the firing behaviors are verified by the neuronal circuits.(3)A generic memristor model with multi-stability is constructed,and a memristive multi-scroll Hopfield neural network is proposed based on the memristor theory.By analyzing the equilibrium points,bifurcation behaviors and attraction basins,the coexisting multi-scroll dynamics in the memristive multi-scroll Hopfield neural network is revealed.The energy transition is found by calculating the average Hamiltonian energy,which provide an explanation for the occurrence of coexisting multi-scroll dynamics.Based on PSIM simulation software and FPGA development platform,the neuronal circuits are designed to verify the multi-scroll dynamics.(4)By introducing the proposed generic memristor into a second-order autonomous system,a three-dimensional autonomous memristive multi-scroll chaotic system is constructed.Multi-scroll dynamics,mega-stable dynamics and extreme event are observed by drawing phase diagram and attraction basins.The occurrences of the mega-stable dynamics and extreme event are fully explained from the perspective of energy,and the circuit implementation is utilized to verify the coexisting dynamics.