Abstract
A novel five-dimensional (5D) memristor-based symmetric circuit, which consists of two symmetric capacitors, two symmetric inductors and only one memristor is presented in this article. The multivariable first order and multivariable second order polynomial functions are used for the internal state function of the memristor respectively. Theoretical and simulation analyses of the novel memristive circuit are investigated using equilibrium points, phase portraits, bifurcation diagrams and Lyapunov exponent spectra, etc. Complex chaotic behaviors are observed and analyzed through simulation results. The first order internal state function memristor-based symmetric circuit system can only exhibit chaotic behavior whereas the second order internal state function memristor-based symmetric circuit system can generate not only chaotic attractors, but also hyperchaotic attractors in proper parameters.
Highlights
Memristor, known as the fourth basic fundamental circuital element in electronic circuits, was first put forward the hypothesis by Leon Chua in 1971 [1]
Some researchers have investigated the hyperchaotic attractor in multi-dimensional circuits systems and memristor-based dynamical circuits systems
The multivariable first order and multivariable second order polynomial functions are used for the internal state function of the memristor respectively
Summary
Known as the fourth basic fundamental circuital element in electronic circuits, was first put forward the hypothesis by Leon Chua in 1971 [1]. Some researchers have investigated the hyperchaotic attractor in multi-dimensional circuits systems and memristor-based dynamical circuits systems. Paper [21] studied the nonlinear dynamics of the TCMNL hyperchaotic oscillator with gyrators based on a smooth mathematical model of the system. A novel memristive hyperchaotic system is presented in paper [26] by introducing a memristor to instead a coupling resistor in the realization of three-dimensional chaotic circuit system.
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