The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network

Usha, K.; Subha, P. A.; Nayak, Chitra R.

doi:10.1016/j.chaos.2018.01.016

Cited by 18 publications

(7 citation statements)

References 54 publications

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“…The speed of variation of z is controlled by r. [23][24][25] The parameter I represents the external stimuli. [26,27] The fourth variable φ denotes magnetic flux across the nerve membrane. A memristor with memductance ρ(φ ) = dq(φ )/dφ is used to realize the coupling between magnetic flux of the field and membrane potential.…”

Section: Modelmentioning

confidence: 99%

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Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

Usha

Subha

2019

Chinese Phys. B

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We analyze the energy aspects of single and coupled Hindmarsh-Rose (HR) neuron models with a quadratic flux controlled memristor. The energy function for HR neuron with memristor has been derived and the dynamics have been analyzed in the presence of various external stimuli. We found that the bursting mode of the system changes with external forcing. The negative feedback in Hamilton energy function effectively stabilizes the chaotic trajectories and controls the phase space. The Lyapunov exponents have been plotted to verify the stabilization of trajectories. The energy aspects during the synchronous dynamics of electrically coupled neurons have been analyzed. As the coupling strength increases, the average energy fluctuates and stabilizes at the point of synchronization. When the neurons are coupled via chemical synapse, the average energy variations show three important regimes: a fluctuating regime corresponding to the desynchronized, a stable region indicating synchronized and a linearly increasing regime corresponding to the amplitude death states have been observed. The synchronization transitions are verified by plotting the transverse Lyapunov exponents. The proposed method has a large number of applications in controlling coupled chaotic systems and in analyzing the energy change during various metabolic processes.

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Section: Modelmentioning

confidence: 99%

“…The transition to the synchronized state is further confirmed by plotting the transverse Lyapunov exponents (TLE). [26] . Figure 14(a) shows the variations of two of the largest TLEs with g e for k 1 = 0.1.…”

Section: Synchronous Dynamics 51 Electrical Couplingmentioning

confidence: 99%

Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

Usha

Subha

2019

Chinese Phys. B

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“…The amount of synchrony in the network is quantified by the term R calculated using the formula in equation (9). The variations in R with g, for different values of δ is shown in figure 6.…”

Section: The Synchronisation Scenariomentioning

confidence: 99%

“…Experimental studies have been carried out to study the synchronisation phenomena in a pair of analogue electronic neurons with electrical and chemical coupling [8]. The transition from a desynchronised to synchronised state though clusterisation has been reported [9,10]. The control of synchrony in a network forms the basis of therapy for certain neurogenetic disorders and also paves the path for emergence of chimera states [11,12].…”

Section: Introductionmentioning

confidence: 99%

Chemically coupled Hindmarsh–Rose neurons with cross interactions between membrane potential and magnetic flux

Remi¹,

Subha²

2023

J. Phys. A: Math. Theor.

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In this work, we have analysed the synchronous dynamics and pattern formation in Hindmarsh-Rose neurons with cross interactions between membrane potential and magnetic flux, in the chemical mode. The self, mixed and cross interactions are realised by varying coupling phase. The magnetic flux induces plateau bursting and amplitude death in the network. The self chemical coupling induces synchrony, whereas, the cross coupling is incapable of it. However, the cross coupling acts along with self coupling to form mixed coupling and induces synchrony in the system. The stability of the synchronous state has been studied by Master stability approach. The parameter space reveals the bifurcation point at which cross coupling overrides self coupling effects. The synchronising ability of interactions are justified in a network of neurons as well. The statistical factor of synchronisation quantifies the amount of synchrony in the network in different interaction modes. The combined effect of non local interactions and mixed coupling of variables initiates the emergence of chimera and multichimera states. However, in cross-coupled systems, only incoherent states are present. The existence of chimera and multichimera states are confirmed by calculating the strength of incoherence and discontinuity measure. The analysis of spatiotemporal patterns reveals the presence of travelling chimeras within the network. The Hamilton energy function indicate that a greater amount of energy is required to sustain coherent neurons at higher potential. This work may enhance the understanding of chimera states and improve its applicability to real-world systems.

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“…Pecora reported an interesting desynchronization state named drum head mode (DHM), which indicates all spokes are synchronized, but the dynamics of the hub are different with spokes. Usha et al established starcoupled system with HindmarshRose (HR) neuron model, and it reported that the DHM state could be found in the unidirectional and bidirectional coupling [45,46].…”

Section: Introductionmentioning

confidence: 99%

Synchronization mode transitions induced by chaos in modified Morris–Lecar neural systems with weak coupling

Wang

et al. 2022

Nonlinear Dyn

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Based on a modified Morris-Lecar neural model, the synchronization modes transitions between two coupled neurons or starcoupled neural network connected by weak electrical and chemical coupling are respectively investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period2 synchronization of action potential of neurons is transformed to desynchronization first, and then to period3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The bifurcation analysis of interspike interval shows that the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period2 synchronization region in the parameters plane is, while the larger the period3 synchronization region will be. For the starcoupled neural network, in the presence of weak electrical coupling, it can exhibit the complete synchronization, desynchronization, and drum head mode states under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized state can not be observed in the starcoupled neural network. Our results might provide novel insights into synchronization modes transition and related biological experiments.

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The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network

Cited by 18 publications

References 54 publications

Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

Chemically coupled Hindmarsh–Rose neurons with cross interactions between membrane potential and magnetic flux

Synchronization mode transitions induced by chaos in modified Morris–Lecar neural systems with weak coupling

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