Initial-dependent extreme multi-stability and offset-boosted coexisting attractors have been significantly concerned recently.This paper constructs a novel five-dimensional(5-D)two-memristor-based dynamical system by ...Initial-dependent extreme multi-stability and offset-boosted coexisting attractors have been significantly concerned recently.This paper constructs a novel five-dimensional(5-D)two-memristor-based dynamical system by introducing two memristors with cosine memductance into a three-dimensional(3-D)linear autonomous dissipative system.Through theoretical analyses and numerical plots,the memristor initial-boosted coexisting plane bifurcations are found and the memristor initial-dependent extreme multi-stability is revealed in such a two-memristor-based dynamical system with plane equilibrium.Furthermore,a dimensionality reduction model with the determined equilibrium is established via an integral transformation method,upon which the memristor initial-dependent extreme multi-stability is reconstituted theoretically and expounded numerically.Finally,physically circuit-implemented PSIM(power simulation)simulations are carried out to validate the plane offset-boosted coexisting behaviors.展开更多
In this paper,a non-autonomous memristive Fitz Hugh-Nagumo(FHN)circuit is constructed using a second-order memristive diode bridge with LC network.For convenience of circuit implementation,an AC voltage source is adop...In this paper,a non-autonomous memristive Fitz Hugh-Nagumo(FHN)circuit is constructed using a second-order memristive diode bridge with LC network.For convenience of circuit implementation,an AC voltage source is adopted to substitute the original AC current stimulus.Stimulated by the slowly varying AC voltage source,the number,locations and stabilities of the equilibrium points slowly evolve with the time,which are thus indicated as the AC equilibrium points.Different sequences of fold and/or Hopf bifurcations are encountered in a full period of time series evolutions,leading to various kinds of chaotic or periodic bursting activities.To figure out the related bifurcation mechanisms,the fold and Hopf bifurcation sets are mathematically formulated to locate the critical bifurcation points.On this basis,the transitions between the resting and repetitive spiking states are clearly illustrated by the time series of the AC equilibrium points and state variables,from which Hopf/sub Hopf,Hopf/Hopf,and Hopf/fold bursting oscillations are identified in the specified parameter regions.Finally,based on a fabricated hardware circuit,the experimental measurements are executed.The results verify that the presented memristive FHN circuit indeed exhibits complex bursting activities,which enriches the family of memristor-based FHN circuits with bursting dynamics.展开更多
Electromagnetic induction effect caused by neuron potential can be mimicked using memristor.This paper considers a fluxcontrolled memristor to imitate the electromagnetic induction effect of adapting feedback synapse ...Electromagnetic induction effect caused by neuron potential can be mimicked using memristor.This paper considers a fluxcontrolled memristor to imitate the electromagnetic induction effect of adapting feedback synapse and presents a memristive neuron model with the adapting synapse.The memristive neuron model is three-dimensional and non-autonomous.It has the time-varying equilibria with multiple stabilities,which results in the global coexistence of multiple firing patterns.Multiple numerical plots are executed to uncover diverse coexisting firing patterns in the memristive neuron model.Particularly,a nonlinear fitting scheme is raised and a fitting activation function circuit is employed to implement the memristive mono-neuron model.Diverse coexisting firing patterns are observed from the hardware experiment circuit and the measured results verify the numerical simulations well.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51777016,51607013,61601062&61801054)。
文摘Initial-dependent extreme multi-stability and offset-boosted coexisting attractors have been significantly concerned recently.This paper constructs a novel five-dimensional(5-D)two-memristor-based dynamical system by introducing two memristors with cosine memductance into a three-dimensional(3-D)linear autonomous dissipative system.Through theoretical analyses and numerical plots,the memristor initial-boosted coexisting plane bifurcations are found and the memristor initial-dependent extreme multi-stability is revealed in such a two-memristor-based dynamical system with plane equilibrium.Furthermore,a dimensionality reduction model with the determined equilibrium is established via an integral transformation method,upon which the memristor initial-dependent extreme multi-stability is reconstituted theoretically and expounded numerically.Finally,physically circuit-implemented PSIM(power simulation)simulations are carried out to validate the plane offset-boosted coexisting behaviors.
基金supported by the National Natural Science Foundation of China(Grant Nos.61601062,51777016,61801054&51607013)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20191451)the Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX19_1764)。
文摘In this paper,a non-autonomous memristive Fitz Hugh-Nagumo(FHN)circuit is constructed using a second-order memristive diode bridge with LC network.For convenience of circuit implementation,an AC voltage source is adopted to substitute the original AC current stimulus.Stimulated by the slowly varying AC voltage source,the number,locations and stabilities of the equilibrium points slowly evolve with the time,which are thus indicated as the AC equilibrium points.Different sequences of fold and/or Hopf bifurcations are encountered in a full period of time series evolutions,leading to various kinds of chaotic or periodic bursting activities.To figure out the related bifurcation mechanisms,the fold and Hopf bifurcation sets are mathematically formulated to locate the critical bifurcation points.On this basis,the transitions between the resting and repetitive spiking states are clearly illustrated by the time series of the AC equilibrium points and state variables,from which Hopf/sub Hopf,Hopf/Hopf,and Hopf/fold bursting oscillations are identified in the specified parameter regions.Finally,based on a fabricated hardware circuit,the experimental measurements are executed.The results verify that the presented memristive FHN circuit indeed exhibits complex bursting activities,which enriches the family of memristor-based FHN circuits with bursting dynamics.
基金supported by the National Natural Science Foundation of China(Grant Nos.51777016 and 61801054)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20191451)。
文摘Electromagnetic induction effect caused by neuron potential can be mimicked using memristor.This paper considers a fluxcontrolled memristor to imitate the electromagnetic induction effect of adapting feedback synapse and presents a memristive neuron model with the adapting synapse.The memristive neuron model is three-dimensional and non-autonomous.It has the time-varying equilibria with multiple stabilities,which results in the global coexistence of multiple firing patterns.Multiple numerical plots are executed to uncover diverse coexisting firing patterns in the memristive neuron model.Particularly,a nonlinear fitting scheme is raised and a fitting activation function circuit is employed to implement the memristive mono-neuron model.Diverse coexisting firing patterns are observed from the hardware experiment circuit and the measured results verify the numerical simulations well.
