Chimera states in ring–star network of Chua circuits

Muni, Sishu Shankar; Provata, A.

doi:10.1007/s11071-020-05910-1

Cited by 29 publications

(14 citation statements)

References 53 publications

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“…Interestingly, double-well chimera state is found in this system. We refer the reader to the author's previous work in [58], where double well chimera state were found in the ring-star network of Chua circuits. Double well chimera state is an important type of chimera state which traverses both the positive and negative values of x state variable.…”

Section: A Characterization Of Chimera Statesmentioning

confidence: 99%

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Muni

Njitacke

Feudjio

et al. 2022

Chaos Theory and Applications

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In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model.

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Section: A Characterization Of Chimera Statesmentioning

confidence: 99%

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Muni

Njitacke

Feudjio

et al. 2022

Chaos Theory and Applications

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“…In previous works, the adaptivity of memristor's conductivity was utilised for the adaptive coupling of CC networks that leads to full coherence [20]. Other forms of system synchronization have been presented with non-adaptive coupling [16], [17] in ring-based networks where the coupling parameters govern the system synchronization regime. Aiming to exploit memristor Xbar's reprogramming for the selective adaptation of coupling, but, meanwhile, to avoid the destructive effect of adaptive memristors that would lead to full coherence, an appealing alternative approach has been utilized.…”

Section: Coupling Chua's Circuitsmentioning

confidence: 99%

“…Of particular interest, the bistable nonlocally-coupled chaotic oscillators, based on Chua's Circuit (CC) [15] have been also considered. These oscillators, when in ring-based network configurations, have been exploited for the generation of complex spatio-temporal patterns that lead to frequency-based [16] and phase-based [17] chimera states.…”

Section: Introductionmentioning

confidence: 99%

“…CC's bistability is evident in the chaotic regime, where the attractor's trajectory oscillates around two certain points and the transition between them is highly dependent on the system's initial conditions, forming the well-known doublescroll attractors in the phase planes. The coupling of CCs has been intensively studied for either system's complete synchronization [18]- [21] or the emergence of richer synchronization regimes, like chimera states [16], [17]. The former case is realised in circuit-level through the adaptivity of novel circuit elements, known as memristors.…”

Section: Introductionmentioning

confidence: 99%

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Emergence of Chimera States with Re-Programmable Memristor Crossbar Arrays

Tsakalos

Ntinas

Karamani

et al. 2021

2021 IEEE International Symposium on Circuits and Systems (ISCAS)

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The time series of the brain are usually characterized by the co-existence of synchronized and desynchronized behaviors. This kind of behavior is related to normal and disorderly functions of the brain. One of the suggested mechanisms to understand thoroughly this behavior are chimera states, which are characterized by the coincidence of coherent and incoherent dynamics that can be exploited through networks of symmetrically coupled identical oscillators. In this work, ring-based networks of Chua's circuits, the simplest electronic oscillators that perform chaotic and well-known bifurcation phenomena, have been extensively studied in memristive crossbars (Xbar), revealing various collective spatio-temporal behaviors, such as chimera states. With respect to different Xbar connectivities and via SPICE-level circuit simulations, the proposed Xbar system proves its efficacy to reproduce spatio-temporal patterns spanning from complete synchronization and chimera states up to fully chaotic states.

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“…Here, We showcase IZH neurons connected in ring and star networks. Next, we also consider a mixed topological network introduced in [11] which is known as ring-star network and study for the prevalence of chimera states. The IZH neurons in all of the networks are non-locally diffusively coupled.…”

Section: Introductionmentioning

confidence: 99%

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

Muni¹,

Rajagopal²,

Karthikeyan³

et al. 2021

Preprint

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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.

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Chimera states in ring–star network of Chua circuits

Cited by 29 publications

References 53 publications

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Emergence of Chimera States with Re-Programmable Memristor Crossbar Arrays

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

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