Bifurcation analyses and hardware experiments for bursting dynamics in non-autonomous memristive FitzHugh-Nagumo circuit

Chen, Mo; Qi, Jianwei; Wu, Huagan; Xu, Quan; Bao, Bocheng

doi:10.1007/s11431-019-1458-5

Cited by 62 publications

(9 citation statements)

References 51 publications

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“…Bao et al [35] implemented the hyperbolic-type memristive Hopfield neural network on breadboard and gave the same results as the numerical simulations. Chen et al [36] verified the bursting dynamics characteristics in nonautonomous memristor Fitzhugh-Nagumo circuit through analog hardware experiment. On the contrary, it is relatively scarce for digital circuits to achieve these neuron models and neural network models.…”

Section: Introductionmentioning

confidence: 98%

Firing mechanism based on single memristive neuron and double memristive coupled neurons

Shen

Wang

et al. 2022

Nonlinear Dyn

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Memristive neurons and memristive neural networks constructed based on memristors have important research significance for revealing the mystery of the brain. This paper proposes a compound hyperbolic tangent cubic nonlinear memristor, which has nonvolatile memory characteristics and local activity characteristics. In particular, the memristor also has three stable pinched hysteresis loops under different initial values. The memristor is applied to Fitzhugh-Nagumo neuron and Hindmarsh-Rose neuron to establish five different memristive neural models, and a series of firing dynamics analysis are carried out on them. At the same time, we not only discuss multiple firing patterns on a single memristive neuron and double memristive coupled neurons, but also compare which neuron and which coupled neural network the proposed memristor is more suitable for, which is a lack of comprehensive investigation in the published research. Furthermore, digital circuit experiment is performed on the FPGA development board to verify the firing mechanism of these memristive neural models, which has potential application value for some practical projects.

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Section: Introductionmentioning

confidence: 98%

Firing mechanism based on single memristive neuron and double memristive coupled neurons

Shen

Wang

et al. 2022

Nonlinear Dyn

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“…Ma et al [27] proposed five different bursting patterns induced by the pitchfork bifurcation delay and Hopf bifurcation delay in a Mathieu-Duffing-van der Pol oscillator. Chen et al [28] analyzed the mechanism of "Hopf/subHopf" bursting, "Hopf/Hopf" bursting and "Hopf/fold" bursting numerically and experimentally based on a non-autonomous memristive FitzHugh-Nagumo oscillator. Vijay et al [29] presented the emergence of the "fold/fold" periodic bursting, intermittent bursting, chaotic bursting oscillation and the route to chaos in the Lienard model.…”

Section: Introductionmentioning

confidence: 99%

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

Zhang

Tang

Wang

2022

Preprint

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This paper investigates the bursting oscillations of a externally and parametrically forced Rayleigh-Duffing oscillator, in which three intermittent bursting types and one normal bursting type, namely intermittent “supHopf/supHopf-supHopf/supHopf” bursting, intermittent “fold/Homoclinic-Homoclinic/supHopf” bursting, intermittent “fold/Homoclinic-supHopf/supHopf” bursting and “fold/Homoclinic” bursting, are analyzed respectively. Recognizing the excitations as slow-varying state variables, the corresponding autonomous system can be exhibited and the bifurcation characteristics is briefly investigated, in particular, the Homoclinic bifurcation is analyzed by means of the Melnikov criterion. This paper shows that the dynamical behaviors of the excited Rayleigh-Duffing oscillator is touchy to the chosen of system parameters, different parameter conditions lead to distinct bifurcation structures that result in the trajectory approaching to different stable attractors and the appearance of different bursting forms. Our study increases the variousness of bursting oscillations and deepens the cognition of the generation mechanism of bursting dynamics. Lastly, the accuracy of the analysis presented in this paper is fully vindicated by the numerical simulations.

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“…Given its potential applications, memristors are conveniently introduced into some existing linear or nonlinear electronic circuits to build various novel memristive chaotic circuits [46]. In this way, numerous mathematical models with different complexities have been proposed in the literature [47][48][49][50][51][52]. On the other hand, the two-dimensional FitzHugh-Nagumo (FHN) model [53,54] is simplified from the four-dimensional Hodgkin-Huxley model for geometrical explanation of neuronal excitability and spiking under excitation.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the two-dimensional FitzHugh-Nagumo (FHN) model [53,54] is simplified from the four-dimensional Hodgkin-Huxley model for geometrical explanation of neuronal excitability and spiking under excitation. Several studies have been performed on the significant and complex dynamical aspects of the FHN model [51,[55][56][57]. rough all these studies, the results showed that the nonautonomous memristive chaotic circuits exhibit rich dynamical behaviors, such as chaos and hyperchaos, coexisting multiple attractors, hidden attractors, and hidden extreme multistability [47][48][49][50][51][52][58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations

et al. 2021

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In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is found that for ω = ν , the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8 , the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors.

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Bifurcation analyses and hardware experiments for bursting dynamics in non-autonomous memristive FitzHugh-Nagumo circuit

Cited by 62 publications

References 51 publications

Firing mechanism based on single memristive neuron and double memristive coupled neurons

Firing mechanism based on single memristive neuron and double memristive coupled neurons

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations

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