Controlling Synchronization of Modified FitzHugh-Nagumo Neurons under External Electrical Stimulation

Mishra, Deepak; Yadav, Abhishek; Ray, Sudipta; Kalra, Prem Kumar

doi:10.14704/nq.2006.4.1.87

Cited by 4 publications

(7 citation statements)

References 11 publications

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“…For details of this stabilizing scheme, see [9]. Since the error dynamics is a polynomial model, the dissipation inequality (3) can be efficiently solved using SDP and SOSTOOLS ( [6], [9], [24], [34] …”

Section: Synchronization Between Two Modelsmentioning

confidence: 99%

“…Recently, synchronization phenomena among multiple subsystems have received much attention in various research fields including neuroscience [24], [30], [31], biology [7], [38], physics [4], [14], [17], [23], [25], [43], coordinated motion and consensus problems [16], [27], control and dynamical systems theory [5], [26], [32], and mechanical engineering [33], [35]. In these areas, it is well known that synchronous behavior among subsystems plays an important role.…”

Section: Introductionmentioning

confidence: 99%

“…Five models have been commonly used to investigate synchronization: the Hodgkin-Huxley [21], [44], Kuramoto [1], [8], [38], Lorenz [17], [23], [41], Fitzhugh-Nagumo [24], [37], and Hindmarsh-Rose [10], [12], [13], [31] models. Note that the first two models are not in polynomial form while the rest are.…”

Section: Introductionmentioning

confidence: 99%

“…For example, coupling functions are proposed for synchronization among particularly connected Fitzhugh-Nagumo models in Refs. [24] and Lorenz models in Refs. [4], [14], [17], [23].…”

Section: Introductionmentioning

confidence: 99%

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A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

Kim¹,

Allgöwer²

2010

Journal of Electrical Engineering and Technology

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-Multiple subsystems are required to behave synchronously or cooperatively in many areas. For example, synchronous behaviors are common in networks of (electro-) mechanical systems, cell biology, coupled neurons, and cooperating robots. This paper presents a feedback scheme for synchronization between Hindmarsh-Rose models which have polynomial vector fields. We show that the problem is equivalent to finding an asymptotically stabilizing control for error dynamics which is also a polynomial system. Then, an extension to a nonlinear observer-based scheme is presented, which reduces the amount of information exchange between models.

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Section: Synchronization Between Two Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…For example, coupling functions are proposed for synchronization among particularly connected Fitzhugh-Nagumo models in Refs. [24] and Lorenz models in Refs. [4], [14], [17], [23].…”

Section: Introductionmentioning

confidence: 99%

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A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

Kim¹,

Allgöwer²

2010

Journal of Electrical Engineering and Technology

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“…Wang et al [15] investigated the synchronization of two coupled neurons, by designing a nonlinear controller, without requiring consideration of the gap junction coupling strength. The response of a system consisting of two FHN neurons, coupled with a gap junction, was investigated, and the significance of the coupling coefficient was studied by Mishra et al [44]. Wang et al [3] studied the synchronization problem of two FHN neuronal systems by proposing nonlinear feedback linearization and adaptive control schemes.…”

Section: Introductionmentioning

confidence: 99%

Complex Synchronization of a Ring-Structured Network of FitzHugh-Nagumo Neurons With Single-and Dual-State Gap Junctions Under Ionic Gates and External Electrical Disturbance

Ibrahim

Jung

2019

IEEE Access

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Synchronization plays an essential role in processing information and decisions by neurons and their networks in the brain, and it is useful to study the synchronization of neuron networks, as a part of the process of understanding the functionality of both healthy and diseased brains. In the past, most studies had developed control schemes relating to synchronization problems which were limited to two or three neurons, which cannot depict the dynamic synchronization behavior of neuron networks. In this paper, we investigated the synchronization issues associated with a ring-structured network of FitzHugh-Nagumo (FHN) neurons, under external electrical stimulation, and with single-and dual-state gap junctions. In addition, the gap junctions (coupling)s and ionic gate disturbances were included in the dynamics of this FHN neuronal network, making our work both more realistic, and more challenging. Thus, each neuron in this network was influenced synaptically by its neighboring two neurons. A simple, robust, and adaptive control scheme, for both a single-and the dual-gap-junction network has been proposed, which will compensate for the nonlinear dynamics without direct cancelation to achieve synchronization. Sufficient conditions to guarantee synchronization of both membrane potentials and recovery variables were derived by using Lyapunov stability theory. Finally, the proposed scheme was validated, and its efficacy was comprehensively analyzed through numerical simulations.

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Bifurcation control of Fitzhugh-Nagumo models

Doruk

Ihnish

2018

SDÜ Fen Bil Enst Der

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A theoretical bifurcation control strategy is presented for a single Fitzhugh-Nagumo (FN) type neuron. The bifurcation conditions are tracked for varying parameters of the individual FN neurons. A MATLAB package called as MATCONT is utilized for this purpose and all parameters of the neuron is analyzed one-by-one. Analysis by MATCONT revealed five Hopf (H) and one Limit-Point/Saddle Point (LP) bifurcation. The Hopf type of bifurcations are controlled by a washout filter supported by projective control theory. Washout filters are designed as first and second order. First order washout filter which is also physically applicable appeared to be more advantageous than the second order version. It appeared that, the LP case could not be stabilized by the aid of a washout filter. To solve this issue, a nonlinear controller is proposed. The only drawback associated with that is its inability to keep the original equilibrium point. Simulations are also provided to validate the research done.

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Controlling Synchronization of Modified FitzHugh-Nagumo Neurons under External Electrical Stimulation

Cited by 4 publications

References 11 publications

A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

A Nonlinear Synchronization Scheme for Hindmarsh-Rose Models

Complex Synchronization of a Ring-Structured Network of FitzHugh-Nagumo Neurons With Single-and Dual-State Gap Junctions Under Ionic Gates and External Electrical Disturbance

Bifurcation control of Fitzhugh-Nagumo models

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