Continuous non-autonomous memristive Rulkov model with extreme multistability*

Xu, Quan; Liu, Tong; Feng, Chengtao; Bao, Han; Wu, Huagan; Bao, Bocheng

doi:10.1088/1674-1056/ac2f30

Cited by 58 publications

(17 citation statements)

References 59 publications

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“…This is the main reason that extreme multistability is often discovered in some circuits and systems involving memory-circuit elements. Intriguingly, extreme multistability has also been discovered in some non-autonomous memristive circuits and systems that have time-varying equilibria [33][34][35][36]. For example, a non-autonomous memristive FitzHugh−Nagumo circuit with its equilibrium points transitioning between no equilibrium point and a line equilibrium set was built, and hidden extreme mulitstability was disclosed [34].…”

Section: Introductionmentioning

confidence: 99%

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

et al. 2022

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Extreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in a simple non-autonomous memcapacitive oscillator in this paper. The oscillator only contains a memcapacitor, a linear resistor, a linear inductor, and a sinusoidal voltage source, which are connected in series. The memcapacitive system model is firstly built for further study. The equilibrium points of the memcapacitive system evolve between a no equilibrium point and a line equilibrium set with the change in time. This gives rise to the emergence of extreme multistability, but the forming mechanism is not clear. Thus, the incremental integral method is employed to reconstruct the memcapacitive system. In the newly reconstructed system, the number and stability of the equilibrium points have complex time-varying characteristics due to the presence of fold bifurcation. Furthermore, the forming mechanism of the extreme multistability is further explained. Note that the initial conditions of the original memcapacitive system are mapped onto the controlling parameters of the newly reconstructed system. This makes it possible to achieve precise control of the extreme multistability. Furthermore, an analog circuit is designed for the reconstructed system, and then PSIM circuit simulations are performed to verify the numerical results.

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Section: Introductionmentioning

confidence: 99%

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

et al. 2022

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“…For normal cases, the nonlinear circuits and systems have several determined equilibrium points and their attractors are self-excited from unstable equilibrium points [20]. However, when having time-varying equilibrium [21][22][23] or line/plane equilibrium [19,[24][25][26][27], the nonlinear circuits and systems demonstrated the coexisting behaviors of infinitely many attractors, resulting in the emergence of special extreme multi-stability.…”

Section: Introductionmentioning

confidence: 99%

Initial-Condition Effects on a Two-Memristor-Based Jerk System

et al. 2022

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Memristor-based systems can exhibit the phenomenon of extreme multi-stability, which results in the coexistence of infinitely many attractors. However, most of the recently published literature focuses on the extreme multi-stability related to memristor initial conditions rather than non-memristor initial conditions. In this paper, we present a new five-dimensional (5-D) two-memristor-based jerk (TMJ) system and study complex dynamical effects induced by memristor and non-memristor initial conditions therein. Using multiple numerical methods, coupling-coefficient-reliant dynamical behaviors under different memristor initial conditions are disclosed, and the dynamical effects of the memristor initial conditions under different non-memristor initial conditions are revealed. The numerical results show that the dynamical behaviors of the 5-D TMJ system are not only dependent on the coupling coefficients, but also dependent on the memristor and non-memristor initial conditions. In addition, with the analog and digital implementations of the 5-D TMJ system, PSIM circuit simulations and microcontroller-based hardware experiments validate the numerical results.

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“…By introducing the nonvolatile locally active memristor into the neural network model composed of three Hopfield neurons, Li et al [27] revealed the coexistence phenomenon of multiple stable modes. Considering the influence of electromagnetic induction and external stimulus, extreme multistability in the continuous non-autonomous memristive Rulkov model was discovered by Xu et al [28]. A new no-equilibrium HR neuron model with memristive electromagnetic induction proposed by Zhang et al [29], which breeds the interesting phenomenon of hidden homogeneous extreme multistability.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of stimuli-based fractional-order memristor-coupled tabu learning two-neuron model and its engineering applications

et al. 2022

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External stimulus has an impact on the functional behavior of the biological nervous system, and appropriate stimulus helps the organism to maintain neural function. Inspired by this, the effects of different external stimuli on the dynamic behaviors of neuron model are studied in this paper. Firstly, a fractional-order(FO) memristor-coupled tabu learning two-neuron model whose equilibrium points are symmetric about the origin and unstable is constructed. The dynamic behaviors of this neuron model under different stimuli is further discussed, which are no external stimulus, external forced current stimulus and electromagnetic radiation (EMR) respectively. The neuron model without external stimulus has periodic attractors, but applying external stimulus to one of the neurons can produce abundant two-scroll chaotic attractors and multistability. Especially, when the neuron model is stimulated by EMR, it can generate hyperchaotic attractors that have not been observed in the tabu learning neuron model before. Besides, the transient transition behaviors of the model under different stimuli are also studied. Then, a pseudo-random number generator (PRNG) is designed and its random performance is tested with NIST suite. Finally, it is applied to voice encryption, and the result shows that it has good encryption effect. Therefore, it can be said that the FO memristor-coupled tabu learning two-neuron model has superior randomness and is suitable for chaotic-based engineering applications.

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Continuous non-autonomous memristive Rulkov model with extreme multistability*

Cited by 58 publications

References 59 publications

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

Initial-Condition Effects on a Two-Memristor-Based Jerk System

Dynamics of stimuli-based fractional-order memristor-coupled tabu learning two-neuron model and its engineering applications

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