Chimera states in a ring of map-based neurons

Khaleghi, Leyla; Panahi, Shirin; Chowdhury, Sayantan Nag; Богомолов, С. А.; Ghosh, Dibakar; Jafari, Sajad

doi:10.1016/j.physa.2019.122596

Cited by 33 publications

(8 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The FHN oscillators on complex networks can model epileptic seizures (Gerster et al, 2020 ). The chimera states also exist in ensembles of bursting Hindmarsh-Rose neurons, even if the coupling is local (Bera et al, 2016 ), and in a discrete neuronal model that was recently developed by Khaleghi et al ( 2019 ) to facilitate an analytic treatment without loss of the essential behavior.…”

Section: The Modelmentioning

confidence: 99%

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

Botha

Ansariara

Emadi

et al. 2022

Front. Comput. Neurosci.

View full text Add to dashboard Cite

The union of the Kuramoto–Sakaguchi model and the Hebb dynamics reproduces the Lisman switch through a bistability in synchronized states. Here, we show that, within certain ranges of the frustration parameter, the chimera pattern can emerge, causing a different, time-evolving, distribution in the Hebbian synaptic strengths. We study the stability range of the chimera as a function of the frustration (phase-lag) parameter. Depending on the range of the frustration, two different types of chimeras can appear spontaneously, i.e., from randomized initial conditions. In the first type, the oscillators in the coherent region rotate, on average, slower than those in the incoherent region; while in the second type, the average rotational frequencies of the two regions are reversed, i.e., the coherent region runs, on average, faster than the incoherent region. We also show that non-stationary behavior at finite N can be controlled by adjusting the natural frequency of a single pacemaker oscillator. By slowly cycling the frequency of the pacemaker, we observe hysteresis in the system. Finally, we discuss how we can have a model for learning and memory.

show abstract

Section: The Modelmentioning

confidence: 99%

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

Botha

Ansariara

Emadi

et al. 2022

Front. Comput. Neurosci.

View full text Add to dashboard Cite

show abstract

“…Investigating the network behaviour of neurons plays a significant role in understanding the synchronous and asynchronous regimes in the coupled neuron network [1,8,9]. Many literatures have shown that the coexistence of both synchronous and asynchronous behaviours plays a vital role in studying the brain neuronal activity [6]. Though there have been many literatures discussing the existence of chimeras in differential equation type Izhikevich neurons [12,5] but less has been the investigation on the map based Izhikevich models.…”

Section: Chimera State In Izh Networkmentioning

confidence: 99%

Discrete hybrid Izhikevich neuron model: nodal and network behaviours considering electromagnetic flux coupling

Muni¹,

Rajagopal²,

Karthikeyan³

et al. 2021

Preprint

View full text Add to dashboard Cite

We analyse the dynamics of the improved discretised version of the well known Izhikevich neuron model under the action of external electromagnetic field. It is found that the three-dimensional IZH map shows rich dynamics. With the variation of the electromagnetic field, period-doubling route to chaos in a repeating fashion is observed from the bifurcation diagram. Even the forward and backward continuation bifurcation diagram which do not completely overlap suggests that there is multistability in the system. The phenomenon of bistability (coexistence of periodic and chaotic attractors) is observed. The presence of periodic and chaotic attractor is aided by the maximal Lyapunov exponent diagram. The Lyapunov phase diagram of electromagnetic field and synapses current shows a large parameter region of chaotic and periodic behaviors with the presence of unbounded regions as well. The IZH map shows a plethora of spiking and bursting patterns such as mixed-mode patterns, tonic spiking, phasic spiking, steady spikes, regular spikes, spike bursting, periodic bursting, phasic bursting, chaotic firing etc with the variation of electromagnetic coupling strength and the synapses current. We also investigate the presence of chimera states in a ring-star, ring, star networks of IZH map neurons. Chimera states are found in the case of ring-star and ring network while synchronised clusters were found in the case of star network and are aided by the spatiotemporal plots, space-time plot, recurrence plots. The rich dynamics shown by the discretised IZH map makes it a promising research model to study about neurodynamics.

show abstract

“…Recently, dynamical systems are found to be an efficient and prominent tool, which open the door to study the role of dynamic interactions in a broad variety of complex systems. The interactions among dynamical systems can give rise to fascinating collective behavior ranging from synchronization [3][4][5] , extreme events 6,7 , chimera states [8][9][10][11][12] , suppression of oscillations [13][14][15] to revival of oscillations 16,17 and many more. Interestingly, most of the previous investigations among dynamical units are confined within the regime of static interactions.…”

Section: Introductionmentioning

confidence: 99%

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Dixit,

Chowdhury,

Prasad

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first order phase transition behavior may change into a second order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for paradigmatic chaotic model of Rössler oscillators and Mac-arthur ecological model.Population biology of ecological networks, person to person communication networks, brain functional networks, possibility of outbreaks and spreading of disease through human contact networks, to name but a few examples which attest to the importance of researches based on temporal interaction approach. Studies based on representating several complex systems as time-varying networks of dynamical units have been shown to be extremely beneficial in understanding real life processes. Surprisingly, in all the previous studies on time-varying interaction, death state receives little attention in a network of coupled oscillators. In addition, only a few studies on dynamic interaction have considered the proximity of the individual systems' trajectories in the context of their interaction. In this paper, we propose a simple yet effective dynamic interaction scheme among nonlinear oscillators, which is capable of relaxing the collective oscillatory dynamics towards the dynamical equilibrium under appropriate choices of parameters. The dynamics of coupled oscillators can show fascinating complex behaviors including various dynamical phenomena. A qualitative explanation of the numerical observation is validated through linear stability analysis and interestingly, a linear stability analysis is persued even when the system is time-dependent. An elaborate study is contemplated to reveal the influences of our proposed dynamic interaction in terms of all the network parameters.

show abstract

Chimera states in a ring of map-based neurons

Cited by 33 publications

References 46 publications

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

Discrete hybrid Izhikevich neuron model: nodal and network behaviours considering electromagnetic flux coupling

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Contact Info

Product

Resources

About