Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

Mehrabbeik, Mahtab; Parastesh, Fatemeh; Ramadoss, Janarthanan; Rajagopal, Karthikeyan; Namazi, Hamidreza; Jafari, Sajad

doi:10.3934/mbe.2021462

Cited by 37 publications

(8 citation statements)

References 49 publications

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“…To quantize the solitary nodes and determine the extent of synchronization in the system after a satisfactory number of iterations, we employ two metrics known as the cross-correlation coefficient [30,55] and the synchronization error [64]. We also realize the complexity of the time series data that get generated from our simulations using a measure known as sample entropy.…”

Section: Quantitative Metrics and Time Series Analysismentioning

confidence: 99%

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

Ghosh

Muni

Fatoyinbo

2023

Preprint

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We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology not only varying in space but also in time. The variation in time is understood by two coupling probabilities, one for the central-peripheral connections and the other for the peripheral-peripheral connections respectively, that update the network topology with each iteration in time. We have further reported the rich spatiotemporal patterns like two-cluster states, chimera states, coherent, and asynchronized states that arise throughout the network dynamics. We have also investigated the appearance of a special kind of asynchronization behavior called "solitary nodes" that have a wide range of applications pertaining to real-world nervous systems. In order to characterize the behavior of the nodes under the influence of these heterogeneities, we have studied two different metrics called the "cross-correlation coefficient" and the "synchronization error". Additionally, to capture the statistical property of the network, for example, how complex the system behaves, we have also studied a measure called "sample entropy". Various two-dimensional color-coded plots are presented in the study to exhibit how these metrics/measures behave with the variation of parameters.

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Section: Quantitative Metrics and Time Series Analysismentioning

confidence: 99%

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

Ghosh

Muni

Fatoyinbo

2023

Preprint

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“…The synchronous firing and chimera state were observed in a ring neuron network constructed with memristorcoupled discrete Chialvo neurons. [34] Mahtab Mehrabbeik et al [35] studied the memristive Rulkov neuron maps and analyzed the synchronous dynamics under electrical and chemical coupling. Their results shows that two m-Rulkov neurons can achieve synchronization only when electrically coupled, but not when chemically coupled.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Yan 晏,

Li 李,

Li 李

2024

Chinese Phys. B

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Research on discrete memristor-based neural networks has received much attention. However, current research mainly focuses on memristor–based discrete homogeneous neuron networks, while memristor-coupled discrete heterogeneous neuron networks are rarely reported. In this study, a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V-I diagram. Based on two-dimensional discrete Izhikevich neuron and two-dimensional discrete Chialvo neuron, a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons. Considering the coupling strength as the control parameter, chaotic firing, periodic firing and hyperchaotic firing patterns are revealed. In particular, multiple coexisting firing patterns are observed, which are induced by different initial values of the memristor. Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength. Furthermore, the effect of Gaussian white noise on synchronization behaviors is also explored. We demonstrate that the presence of noise not only leads to the transition of firing patterns, but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

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“…Sausedo-Solorio and Pisarchik [22] considered the Rulkov maps with memory and synaptic delay and observed lag or anticipated synchronization. The network of the memristive version of the Rulkov model was studied by Mehrabbeik et al [23]. They showed that in contrast to the original Rulkov models, two electrically coupled memristive Rulkov maps could reach complete synchronization.…”

Section: Introductionmentioning

confidence: 99%

Synchronization in a network of map-based neurons with memristive synapse

Wang

Tian

Krejcar

et al. 2022

Eur. Phys. J. Spec. Top.

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The synchronization of coupled neurons has been an important field of study in neuroscience. In this paper, the synchronization in coupled map-based neurons is studied. It is assumed that the neurons are coupled via a memristor. Firstly, the case of two-coupled neurons is investigated, and then two neurons are used as the units of a ring network. It is shown that the memristive coupling coefficient and the initial condition of the flux variable affect the synchronization of two neurons. By increasing the memristive coupling coefficient, multiple synchronous and asynchronous regions are observed. In the ring network, two neurons in each unit can become synchronous, but the whole network does not reach complete synchronization.

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Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

Cited by 37 publications

References 49 publications

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Synchronization in a network of map-based neurons with memristive synapse

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