Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil’nikov approach

Wei, Wei; Zuo, Mingzhang

doi:10.1088/1674-1056/24/8/080501

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…Since e 1 (k), e 2 (k), and e 3 (k) asymptotically approach zero (see Fig. 6), equation (23) highlights that each drive system state is synchronized with a linear combination of response systems states, indicating that IFSHPS has been successfully achieved. 19) and (20).…”

Section: Example 2: N > Mmentioning

confidence: 98%

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

Ouannas

Grassi

2016

Chinese Phys. B

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A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Hénon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Hénon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).

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Section: Example 2: N > Mmentioning

confidence: 98%

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

Ouannas

Grassi

2016

Chinese Phys. B

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“…HR is a fundamental single-neuron model for the explanation of the dynamical properties of neurons, and its three-dimensional (3D) nonlinear ordinary differential equations can be described as below [36][37][38]:…”

Section: Hindmarsh-rose Neural Modelmentioning

confidence: 99%

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

Xu,

Zhang,

et al. 2023

Phys. Scr.

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This paper investigates the occurrence of stochastic resonance in the three-dimensional Hindmarsh-Rose (HR) neural model driven by both multiplicative and additive Gaussian noise. Firstly, the three-dimensional HR neural model is transformed into the one-dimensional Langevin equation of the HR neural model using the adiabatic elimination method, and the effects of HR neural model parameters on the potential function are analyzed. Secondly the Steady-state Probability Density (SPD), the Mean First-Passage Time (MFPT), and the Signal-to-Noise Ratio (SNR) of the HR neural model are derived, based on two-state theory. Then, the effects of different parameters (a, b, c, s), noise intensity, and the signal amplitude on these metrics are analyzed through theoretical simulations, and the behavior of particles in a potential well is used to analyze how to choose the right parameters to achieve high-performance stochastic resonance. Finally, numerical simulations conducted with the fourth-order Runge–Kutta algorithm demonstrate the superiority of the HR neural model over the classical bistable stochastic resonance (CBSR) in terms of performance. The peak SNR of the HR neural model is 0.63 dB higher than that of the CBSR system. Simulation results indicate that the occurrence of stochastic resonance occur happens in HR neural model under different values of parameters. Furthermore, under certain conditions, there is a ‘suppress’ phenomenon that can be produced by changes in noise, which provides great feasibilities and practical value for engineering application.

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“…It is worth noting with the excitement that there has been a great deal of research on complexity science by the Chinese physical community, including works on stochastic resonance, bifurcations, and chaos. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Mathematically, multifractals are characterized by many or infinitely many power-law relations. In this paper, we work with a specific type of multifractal, called the random multiplicative process model, to analyze the color value and the clarity degree.…”

Section: Introductionmentioning

confidence: 99%

Multifractal modeling of the production of concentrated sugar syrup crystal

Bi¹,

Gao

2016

Chinese Phys. B

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High quality, concentrated sugar syrup crystal is produced in a critical step in cane sugar production: the clarification process. It is characterized by two variables: the color of the produced sugar and its clarity degree. We show that the temporal variations of these variables follow power-law distributions and can be well modeled by multiplicative cascade multifractal processes. These interesting properties suggest that the degradation in color and clarity degree has a systemwide cause. In particular, the cascade multifractal model suggests that the degradation in color and clarity degree can be equivalently accounted for by the initial "impurities" in the sugarcane. Hence, more effective cleaning of the sugarcane before the clarification stage may lead to substantial improvement in the effect of clarification.

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Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil’nikov approach

Cited by 4 publications

References 16 publications

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

Multifractal modeling of the production of concentrated sugar syrup crystal

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