From complete to modulated synchrony in networks of identical Hindmarsh-Rose neurons

Ehrich, Sebastian; Pikovsky, Arkady; Rosenblum, Michael G.

doi:10.1140/epjst/e2013-02025-8

Cited by 10 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5). This noiseinduced rhythm switching is different from other mechanisms of coupling-induced dephasing [47,51,52], where noise does not play a key role. We note a similarity to Brownian motions in tilted periodic potentials where the diffusion coefficient becomes nonmonotonous and greatly amplified at a critical tilt [53,54].…”

Section: Discussioncontrasting

confidence: 74%

Robust design of polyrhythmic neural circuits

2014

View full text Add to dashboard Cite

Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.

show abstract

Section: Discussioncontrasting

confidence: 74%

Robust design of polyrhythmic neural circuits

2014

View full text Add to dashboard Cite

show abstract

“…( ) so that smooth interaction functions necessarily lead to effectively stable two-cluster states (at least with respect to intracluster perturbations). Even more, equation (27) yields that in the biharmonic model no effectively unstable cluster may exist: only HCs. For these clusters to exist, higher harmonics are needed.…”

Section: Lif Neuronsmentioning

confidence: 99%

“…A variant of quasiperiodic partially synchronous dynamics has been detected in models beyond phase approximation, i.e. in globally coupled Hindmarsh-Rose neurons and Stuart-Landau oscillators; here the macroscopic and microscopic frequencies are equal only on average, but the motion of oscillators is additionally modulated by a generally incommensurate frequency [26,27].…”

Section: Introductionmentioning

confidence: 99%

A minimal model of self-consistent partial synchrony

2016

Self Cite

View full text Add to dashboard Cite

In the body of the paper we have spotted three minor errors that do not affect the overall results and have to be corrected as follows:(A) Z m as defined in equations (10) and (12) coincide with the usual Kuramoto-Daido order parameters (see equation (3)), only once they have been multiplied by 2p. All formulas concerning the stability of SCPS remain unchanged, while the expression of the exponent 1 d , controlling the stability of the splay state (see equation (6)) must be divided by 2p, i.e. AbstractWe show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field.

show abstract

“…Among all kinds of networks, biological neural network is a persistent and hot topic. In the past decade, a lot of studies have been devoted to the synchronization of all kinds of neural networks under different conditions (Li et al 2003 ; Cao and Lu 2006 ; Yu et al 2009 ; Ehrich et al 2013 ; Fan et al 2018 ; Kong and Sun 2021 ; Wouapi et al 2020 ) because of studies have shown that Parkinson’s, epilepsy and other brain deficits are caused by the damage to the ability of neurons to synchronize with their neighbors. As shown in Njitacke et al ( 2021 ), the synchronization of neurons under different structures and parameters were conducted according to the state estimation error system and the control strategy.…”

Section: Introductionmentioning

confidence: 99%

Topology identification and dynamical pattern recognition for Hindmarsh–Rose neuron model via deterministic learning

Chen

Zeng

et al. 2022

Cogn Neurodyn

View full text Add to dashboard Cite

Studies have shown that Parkinson’s, epilepsy and other brain deficits are closely related to the ability of neurons to synchronize with their neighbors. Therefore, the neurobiological mechanism and synchronization behavior of neurons has attracted much attention in recent years. In this contribution, it is numerically investigated the complex nonlinear behaviour of the Hindmarsh–Rose neuron system through the time responses, system bifurcation diagram and Lyapunov exponent under different system parameters. The system presents different and complex dynamic behaviors with the variation of parameter. Then, the identification of the nonlinear dynamics and topologies of the Hindmarsh–Rose neural networks under unknown dynamical environment is discussed. By using the deterministic learning algorithm, the unknown dynamics and topologies of the Hindmarsh–Rose system are locally accurately identified. Additionally, the identified system dynamics can be stored and represented in the form of constant neural networks due to the convergence of system parameters. Finally, based on the time-invariant representation of system dynamics, a fast dynamical pattern recognition method via system synchronization is constructed. The achievements of this work will provide more incentives and possibilities for biological experiments and medical treatment as well as other related clinical researches, such as the quantifying and explaining of neurobiological mechanism, early diagnosis, classification and control (treatment) of neurologic diseases, such as Parkinson’s and epilepsy. Simulations are included to verify the effectiveness of the proposed method.

show abstract

From complete to modulated synchrony in networks of identical Hindmarsh-Rose neurons

Cited by 10 publications

References 18 publications

Robust design of polyrhythmic neural circuits

Robust design of polyrhythmic neural circuits

A minimal model of self-consistent partial synchrony

Topology identification and dynamical pattern recognition for Hindmarsh–Rose neuron model via deterministic learning

Contact Info

Product

Resources

About