Combinatorics

Physics

Nonlinear system

Attractor

Topology (electrical circuits)

Bifurcation

Mathematics

Bifurcation diagram

Statistical physics

Phase portrait

Memristor

Limit (mathematics)

Mathematical analysis

Artificial intelligence

Control (management)

Lyapunov exponent

Chaotic

Multistability

Computer science

Quantum mechanics

Differential equation

Equilibrium point

Control theory (sociology)

Limit cycle

International Journal of Bifurcation and Chaos

A memristor with coexisting pinched hysteresis loops and twin local activity domains is presented and analyzed, with an emulator being designed and applied to the classic Chua’s circuit to replace the diode. The memristive system is modeled with four coupled first-order autonomous differential equations, which has three equilibria determined by three static equilibria of the memristor but not controlled by the system parameters. The complex dynamics of the system are analyzed by using compound coexisting bifurcation diagrams, Lyapunov exponent spectra and phase portraits, including point attractors, limit cycles, symmetrical chaotic attractors and their blasting, extreme multistability, state-switching without parameter, and transient chaos. Of particular surprise is that the extreme multistability of the system is hidden and symmetrically distributed. It is found that the existence of transient chaos in the specified parameter domain is determined by using bifurcation diagrams within different time durations and Lyapunov exponents with chaotic sequences. Finally, the symmetrical chaotic attractor and the system blasting are verified by digital signal processing experiments, which are consistent with the numerical analysis.

Extreme Multistability and Complex Dynamics of a Memristor-Based Chaotic System