Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons.In this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse,are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh-Rose neuron model.Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns.The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors.Finally,the simulation circuit and DSP hardware implementation results validate the physical mechanism,as well as the reliability of the biological neuron model.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

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.

Multistability and coexisting transient chaos in a simple memcapacitive system

The self-excited attractors and hidden attractors in a memcapacitive system which has three elements are studied in this paper.The critical parameter of stable and unstable states is calculated by identifying the eigenvalues of Jacobian matrix.Besides,complex dynamical behaviors are investigated in the system,such as coexisting attractors,hidden attractors,coexisting bifurcation modes,intermittent chaos,and multistability.From the theoretical analyses and numerical simulations,it is found that there are four different kinds of transient transition behaviors in the memcapacitive system.Finally,field programmable gate array(FPGA)is used to implement the proposed chaotic system.

Optical bistability and multistability in a three-level △-type atomic system under the nonresonant condition

Under a nonresonant condition, we theoretically investigate hybrid absorptive-dispersive optical bistability and multistability behaviours in a three-level △-type system by using a microwave field to drive a hyperfine transition between two upper excited states inside a unidirectional ring cavity. We find that the optical bistability and multistability behaviours can be controlled by adjusting the intensity of the microwave field or the intensity of the coherent coupling field. Furthermore, our studies show an interesting phenomenon of the transition from the optical bistability to the optical multistability only by changing the negative detuning of the coupling field into the positive detuning of the coupling field.

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current.Then,based on the classical Liu-Chen system,a new memristor-based fourdimensional(4D)chaotic system is designed by using the five-value memristor.The trajectory phase diagram,Poincare mapping,bifurcation diagram,and Lyapunov exponent spectrum are drawn by numerical simulation.It is found that,in addition to the general chaos characteristics,the system has some special phenomena,such as hidden homogenous multistabilities,hidden heterogeneous multistabilities,and hidden super-multistabilities.Finally,according to the dimensionless equation of the system,the circuit model of the system is built and simulated.The results are consistent with the numerical simulation results,which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.

Heterogeneous dual memristive circuit:Multistability,symmetry,and FPGA implementation

An improved heterogeneous dual memristive circuit(DMC)is proposed based on Chua's circuit,which shows good symmetry and multistablility.For the difficulty in controlling the initial conditions,which restricts the engineering applications,the 3 rd-order model(3 OM)in flux-charge domain is derived from the 5 th-order model(5 OM)in volt-ampere domain by using the flux-charge analysis method(FCAM).The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram,Lyapunov exponents,and especially attraction basins.The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit.To avoid the noise in the analog circuit,a field-programmable gate array(FPGA)is utilized to realize the reduction model,which is rarely reported and valuable for relevant research and application.

Stability and multistability of synchronization in networks of coupled phase oscillators

Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state.Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.

Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginarytype activation functions

In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.

Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability

Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula.The boundness condition of the proposed hyperchaotic system is proved.Coexisting bifurcation diagram and numerical verification explain the bistability.The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin.The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS.The NIST tests show that the generated signal sequence is highly random,which is feasible for encryption purposes.Furthermore,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.

Optical bistability and multistability via double dark resonance in graphene nanostructure

Electrons in graphene nanoribbons can lead to exceptionally strong optical responses in the infrared and terahertz regions owing to their unusual dispersion relation.Therefore,on the basis of quantum optics and solid-material scientific principles,we show that optical bistability and multistability can be generated in graphene nanostructure under strong magnetic field.We also show that by adjusting the intensity and detuning of infrared laser field,the threshold intensity and hysteresis loop can be manipulated efficiently.The effects of the electronic cooperation parameter which are directly proportional to the electronic number density and the length of the graphene sample are discussed.Our proposed model may be useful for the nextgeneration all-optical systems and information processing based on nano scale devices.

Optical bistability and multistability in a defect slab doped by GaAs/AlGaAs multiple quantum wells

We proposed a new model for controlling the optical bistability（OB） and optical multistability（OM） in a defect slab doped with four-level GaAs/AlGaAs multiple quantum wells with 15 periods of 17.5 nm GaAs wells and 15-nm Al_（0.3）Ga_（0.7）As barriers. The effects of biexciton energy renormalization, exciton spin relaxation, and thickness of the slab on the OB and OM properties of the defect slab were theoretically investigated. We found that the transition from OB to OM or vice versa is possible by adjusting the controllable parameters in a lab. Moreover, the transmission, reflection, and absorption properties of the weak probe light through the slab were also discussed in detail.

Optical bistability and multistability via atomic coherence in the quasi-Λ-type atomic system

The steady-state optical bistability(OB) and optical multistability(OM) behavior in the quasi——type atomic system driven by a probe field and a coherent coupling field inside a unidirectional ring cavity are shown,and the effects of coupling-field detuning and coupling-field intensity on the OB and OM behavior are investigated. The transition from OB to OM or vice versa is found by varying the detuning of the coherent coupling field or by adjusting the intensity of the coupling field. The influence of the atomic cooperation parameter on the OM behavior is also discussed.

Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator

Extreme multistability has seized scientists’ attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper, a four-dimensional(4D) memcapacitive oscillator is built using four linear circuit elements and one nonlinear charge-controlled memcapacitor with a cosine inverse memcapacitance. The 4D memcapacitive oscillator possesses a line equilibrium set, and its stability periodically evolves with the initial condition of the memcapacitor. The 4D memcapacitive oscillator exhibits initial-condition-switched boosting extreme multistability due to the periodically evolving stability. Complex dynamical behaviors of period doubling/halving bifurcations, chaos crisis, and initial-condition-switched coexisting attractors are revealed by bifurcation diagrams, Lyapunov exponents, and phase portraits. Thereafter, a reconstructed system is derived via integral transformation to reveal the forming mechanism of the initial-condition-switched boosting extreme multistability in the memcapacitive oscillator. Finally, an implementation circuit is designed for the reconstructed system, and Power SIMulation(PSIM) simulations are executed to confirm the validity of the numerical analysis.

Optical bistability and multistability via multi-Raman-channel interference

We investigate the optical bistability and multistability behaviors in a closed three-level A-type atomic system. By adding a sideband on either hand of the transitions which are originally coupled by a coherent control field and a coherent probe field to disturb the two-photon resonance, bistability occurs due to two-channel interference. Increasing the sideband Rabi frequency leads to the switching from bistability to tristability. When the sideband simultaneously couples with both hands, we can easily obtain quadrastability.

Controllable optical multistability in hybrid optomechanical system assisted by parametric interactions

We theoretically investigate the multistable behavior of a hybrid optomechanical system, in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical parametric amplifier （OPA）. It is shown that the multistable behavior of the mean intracavity photon number can be controlled flexibly by adjusting the nonlinear gain parameter of the OPA, the phase of the field pumping the OPA, the power and frequency of the field driving the cavity, and the Coulomb coupling strength between the two charged mechanical resonators. In particular, the increase of the nonlinear gain parameter can result in a transition from bistability to tristability. Moreover, the effect of the Coulomb coupling strength on the bistable behavior of the steady-state positions of the two mechanical resonators is discussed.

Optical bistability and multistability via amplitude and phase control in a Duplicated two-level system

We investigate the optical bistabiiity （OB） in a duplicated two-level system contained in a ring cavity. The atoms are driven by two orthogonally polarized fields with a relative phase. The OB behavior of such a system can be controlled by the amplitude and the relative phase of the coupling field, and it is possible to switch between bistabilitv and multistability by adjusting the relative phase.

A novel variable-order fractional chaotic map and its dynamics

In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.

Multistate transition and coupled solid-liquid modeling of motion process of long-runout landslide

The recognition,repetition and prediction of the post-failure motion process of long-runout landslides are key scientific problems in the prevention and mitigation of geological disasters.In this study,a new numerical method involving LPF3D based on a multialgorithm and multiconstitutive model was proposed to simulate long-runout landslides with high precision and efficiency.The following results were obtained:(a)The motion process of landslides showed a steric effect with mobility,including gradual disintegration and spreading.The sliding mass can be divided into three states(dense,dilute and ultradilute)in the motion process,which can be solved by three dynamic regimes(friction,collision,and inertial);(b)Coupling simulation between the solid grain and liquid phases was achieved,focusing on drag force influences;(c)Different algorithms and constitutive models were employed in phase-state simulations.The volume fraction is an important indicator to distinguish different state types and solid‒liquid ratios.The flume experimental results were favorably validated against long-runout landslide case data;and(d)In this method,matched dynamic numerical modeling was developed to better capture the realistic motion process of long-runout landslides,and the advantages of continuum media and discrete media were combined to improve the computational accuracy and efficiency.This new method can reflect the realistic physical and mechanical processes in long-runout landslide motion and provide a suitable method for risk assessment and pre-failure prediction.