Collective dynamics of neural network with distance dependent field coupling

Abstract

In this work, we analyse the collective dynamics of Hindmarsh-Rose neurons with distance dependent memristor and mean field coupling, realised by power law exponent. The memristor characterises the electromagnetic field induced by the magnetic flux. The mean field represents the global effect in the neurons which are usually influenced by enormous number of neighbours. The uniform global mean field drives the memristive neural network from Amplitude Death to synchronised bursting state. Desynchronised, Mixed Oscillatory, imperfect and complete synchronised states are attained by the network due to the interplay between memristor and uniform mean field coupling. The synchronisation scenario has been analysed in distance dependent memristive and mean field network, by varying the values of power law exponent. The distance dependent mean field coupling induces chimera and multichimera states in the system. The strength of incoherence and discontinuity measure are calculated to distinguish incoherent, chimera, multichimera and coherent states. Coherent states are unattainable for high values of power law exponent. The existence of chimera states in system with long range interactions are verified by parameter space. This work may give better understanding about the different aspects of synchronisation involved in neural networks with distance dependent coupling and proves that the non local synaptic coupling is not a prerequisite to realise chimera states.