A novel memristor-based chaotic system with line equilibria and its complex dynamics

Abstract

Memristor, as a nonlinear element, provides many advantages thanks to its superior properties to design different chaotic circuits. Thus, a novel four-dimensional double-scroll chaotic system with line equilibria as well as two unstable equilibria based on the flux-memristor model is proposed in this paper. The effects of initial values and parameters on the dynamic characteristics of the system are studied in detail by means of phase diagrams, Lyapunov exponent spectrums, bifurcation diagrams, two-parameter bifurcation diagrams and basins of attraction. Besides, a series of complex phenomena in the system, such as sustained chaos, bistability, transient chaos and coexisting attractors are observed, proving that the chaotic system has rich dynamic characteristics. Also, spectral entropy (SE) complexity algorithm and [Formula: see text] complexity algorithm based on structure complexity are adopted to analyze the complexity of the system. Additionally, PSPICE circuit simulation and Micro-Controller Unit (MCU) hardware experiment are carried out to verify the correctness of theoretical analysis and numerical simulation. Finally, the pulse chaos synchronization is achieved from the perspective of maximum Lyapunov exponent, and numerical simulations demonstrate the occurrence of the proposed system and practicability of the pulse synchronization control.

Integrated Circuit of a Chua’s System Based on the Integral-Differential Nonlinear Resistance with Multi-Path Voltage-Controlled Oscillator

“…The anti-interference and anti-interception ability of the sequence is enhanced as its complexity increases. The comparison of complexity in chaotic systems is typically conducted through various methods, such as phase diagram observation and the measurement of Lyapunov exponents and entropy [ 40 , 41 , 42 ]. The observation of the phase diagram can only provide an approximation of the intricate nature of the chaotic system.…”

Coexisting firing patterns and circuit design of locally active memristive autapse morris-lecar neuron

“…When other parameters take the values in section 3.1, The system equilibrium point is S 1 = (−0.20000000, 0.00000614, 0.00905513k−0.04409059, 1.164396870), S 2 = (−0.20000000, 0.00000614, 0.03897646k−0.04409059, −0.04679673) and S 3 = (−0.20000000, 0.00000614, −0.01203160k−0.04409059, −0.91760013). According to equations (8)- (11), the Jacobian matrix of the locally active memristor neuron system at the equilibrium point S is…”

“…Since the concept of memristor was put forward by Professor Chua [7] in 1971 to the successful development of physical memristor by HP Labs [8] in 2008, memristor has been put into use in many areas like chaotic circuit [9][10][11][12], image processing [13][14][15][16][17], neural network [18][19][20][21][22][23] and non-volatile memory [24][25][26][27], etc And its bionic function provides a new idea for the study of neurodynamics. The use of memristor to describe the effect of electromagnetic induction on neuronal system can reveal the firing pattern transition and bifurcating mechanism of neuronal system under electromagnetic action [28][29][30][31].…”