Continuous non-autonomous memristive Rulkov model with extreme multistability

Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and external stimulus are simultaneously considered herein.The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current.Thus,the presented model possesses a line equilibrium set evolving over the time.The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed.Afterwards,numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction,external stimulus,and initial conditions.Interestingly,the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model.Furthermore,an analog circuit of the proposed model is implemented,upon which the hardware experiment is executed to verify the numerically simulated extreme multistability.The extreme multistability is numerically revealed and experimentally confirmed in this paper,which can widen the future engineering employment of the Rulkov model.

Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance

A four-dimensional memristive system is constructed using a novel ideal memristor with cosine memductance. Due to the special memductance nonlinearity, this memristive system has a line equilibrium set(0, 0, 0, δ) located along the coordinate of the inner state variable of the memristor, whose stability is periodically varied with a change of δ. Nonlinear and one-dimensional initial offset boosting behaviors, which are triggered by not only the initial condition of the memristor but also other two initial conditions, are numerically uncovered. Specifically, a wide variety of coexisting attractors with different positions and topological structures are revealed along the boosting route. Finally, circuit simulations are performed by Power SIMulation(PSIM) to confirm the unique dynamical features.