Recovery of hidden information through synaptic dynamics

Rabinovich, M. I.; Pinto, Reynaldo D.; Tumer, Evren; Stiesberg, Gregg; Huerta, Ramón; Selverston, Allen I.

doi:10.1088/0954-898x_13_4_304

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…where N is given by Eq. (19). Equation 24gives us an energy function which is unique to the error dynamical system of our coupled neurons, and it gives us information about the energy dissipated during the synchronization dynamics.…”

Section: Synchronization Energy and Hamilton Functionmentioning

confidence: 99%

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Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

Yamakou

2020

Nonlinear Dyn

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In this paper, we consider a 5-dimensional Hindmarsh-Rose neuron model. This improved version of the original model shows rich dynamical behaviors, including a chaotic super-bursting regime. This regime promises a greater information encoding capacity than the standard bursting activity. Based on the Krasovskii-Lyapunov stability theory, the sufficient conditions (on the synaptic strengths and magnetic gain parameters) for stable chaotic synchronization of the model are obtained. Based on Helmholtz's theorem, the Hamilton function of the corresponding error dynamical system is also obtained. It is shown that the time variation of this Hamilton function along trajectories can play the role of the time variation of the Lyapunov function-in determining the stability of the synchronization manifold. Numerical computations indicate that as the synaptic strengths and the magnetic gain parameters change, the time variation of the Hamilton function is always nonzero (i.e., a relatively large positive or negative value) only when the time variation of the Lyapunov function is positive, and zero (or vanishingly small) only when the time variation of the Lyapunov function is also zero. This, therefore, paves an alternative way to determine the stability of synchronization manifolds and can be particularly useful for systems whose Lyapunov function is difficult to con

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Section: Synchronization Energy and Hamilton Functionmentioning

confidence: 99%

“…This extension of the phase space dimension from 3D to 4D also increased the complexity of the model; thereby enabling the 4D model to capture the larger chaotic regime of real biological neurons [13][14][15]. Detailed bifurcation analysis of the 4D HR neuron model can be found in [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

Yamakou

2020

Nonlinear Dyn

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Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator

Ngouonkadi¹,

Fotsin²,

Fotso³

et al. 2016

Chaos, Solitons & Fractals

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We report on the bifurcation analysis of an extended Hindmarsh-Rose (eHR) neuronal oscillator. We prove that Hopf bifurcation occurs in this system, when an appropriate chosen bifurcation parameter varies and reaches its critical value. Applying the normal form theory, we derive a formula to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic flows. To observe this latter bifurcation and to illustrate its theoretical analysis, numerical simulations are performed. Hence, we present an explanation of the discontinuous behavior of the amplitude of the repetitive response as a function of system's parameters based on the presence of the subcritical unstable oscillations. Furthermore, the bifurcation structures of the system are studied, with special care on the effects of parameters associated with the slow current and the slower dynamical process. We find that the system presents diversity of bifurcations such as period-doubling, symmetry breaking, crises and reverse period-doubling, when the afore mentioned parameters are varied in tiny steps. The complexity of the bifurcation structures seems useful to understand how neurons encode information or how they respond to external stimuli. Furthermore, we find that the extended Hindmarsh-Rose model also presents the multistability of oscillatory and silent regimes for precise sets of its parameters. This phenomenon plays a practical role in short-term memory and appears to give an evolutionary advantage for neurons since they constitute part of multifunctional microcircuits such as central pattern generators.

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Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

et al. 2015

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Recovery of hidden information through synaptic dynamics

Cited by 5 publications

References 27 publications

Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator

Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

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