Chaos is an interesting nonlinear phenomenon that focuses on the behavior of dynamical systems that are highly sensitive to initial conditions. Additionally, it can be obtained from a class of nonlinear dynamical systems described by a set of autonomous ordinary differential equations. Basically, intricate nonlinear phenomena in various nonlinear dynamical systems can be experimentally measured and successfully validated from the implementation circuits. Memristor-based nonlinear dynamical system easily presents the initial condition dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors, which has been receiving much research attention in recent years. Recently published papers have highlighted the emergence of extreme multistability which has been seen to affect the engineering applicability of the nonlinear dynamical system, and has also generated challenges for the switching controls of the multiple stable states. Therefore, it is imperative that an investigation of the coexisting multiple or infinitely many attractors and the corresponding physical hardware implementation be undertaken as it would play a vital role in theoretical studies and information engineering applications.
Changzhou University scientists: Han Bao (PhD candidate), Ning Wang (PhD candidate), Professor Bocheng Bao, Associate professor Mo Chen at in collaboration with Ms Peipei Jin, Professor Guangyi Wang at Hangzhou Dianzi University introduced an ideal and active flux-controlled memristor with absolute value nonlinearity into an existing hypogenetic chaotic jerk system. Their work is currently published in the research journal, Communications in Nonlinear Science and Numerical Simulation.
Briefly, the research method employed commenced with the introduction of the novel memristor-based hypogenetic jerk system with four-line equilibria, after which the stability of the four-line equilibria were explored. Next, the researchers investigated the initial conditions dependent extreme multistability by bifurcation diagrams and Lyapunov exponent spectra. Lastly, they designed an implementation circuit and performed PSIM (Power Simulation) circuit simulations in order to verify the initial conditions-dependent dynamical behaviors of coexisting infinitely many attractors and transient period in the memristive hypogenetic jerk system.
The authors observed that the coexisting infinitely many attractors’ behavior was revealed by attraction basins and phase portraits. The research team also noted that the unusual transition behavior of long-term transient period with steady chaos, entirely different from the phenomenon of transient chaos, was found for some initial conditions. Moreover, from the hardware circuit designed and fabricated, the truth of extreme multistability was verified.
In a nutshell, the study presented an interesting memristor-based chaotic system with hypogenetic jerk equation and circuit forms, which was constructed by introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system. Generally, they observed that the system had four-line equilibria and exhibited an initial condition-dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors. Altogether, it can be concluded that the limit cycles and chaotic attractors exhibited in the memristor based hypogenetic jerk system are all self-existed attractors, rather than hidden attractors.
Han Bao, Ning Wang, Bocheng Bao, Mo Chen, Peipei Jin, Guangyi Wang. Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria. Communications in Nonlinear Science and Numerical Simulation Volume 57, 2018, Pages 264-275Go To Communications in Nonlinear Science and Numerical Simulation