Alternating chimeras in networks of ephaptically coupled bursting neurons

Abstract

The distinctive phenomenon of the chimera state has been explored in neuronal systems under a variety of different network topologies during the last decade. Nevertheless, in all the works, the neurons are presumed to interact with each other directly with the help of synapses only. But, the influence of ephaptic coupling, particularly magnetic flux across the membrane, is mostly unexplored and should essentially be dealt with during the emergence of collective electrical activities and propagation of signals among the neurons in a network. Through this article, we report the development of an emerging dynamical state, namely, the , in a network of identical neuronal systems induced by an external electromagnetic field. Owing to this interaction scenario, the nonlinear neuronal oscillators are coupled indirectly via electromagnetic induction with magnetic flux, through which neurons communicate in spite of the absence of physical connections among them. The evolution of each neuron, here, is described by the three-dimensional Hindmarsh-Rose dynamics. We demonstrate that the presence of such non-locally and globally interacting external environments induces a stationary alternating chimera pattern in the ensemble of neurons, whereas in the local coupling limit, the network exhibits a transient chimera state whenever the local dynamics of the neurons is of the chaotic square-wave bursting type. For periodic square-wave bursting of the neurons, a similar qualitative phenomenon has been witnessed with the exception of the disappearance of cluster states for non-local and global interactions. Besides these observations, we advance our work while providing confirmation of the findings for neuronal ensembles exhibiting plateau bursting dynamics and also put forward the fact that the plateau pattern actually favors the alternating chimera more than others. These results may deliver better interpretations for different aspects of synchronization appearing in a network of neurons through field coupling that also relaxes the prerequisite of synaptic connectivity for realizing the chimera state in neuronal networks.

Quantum Calcium-Ion Interactions with EEG

“…There are other possible sources of magnetic vector potentials not described as wires with currents [44]. Their net effects plausibly would be included the vector magnetic potential of net synchrous firings, but not their functional forms as derived here.…”

Astroglial Isopotentiality and Calcium-Associated Biomagnetic Field Effects on Cortical Neuronal Coupling

“…One of the proposed mechanisms of synchronization is the communication through resonance that suggests that oscillations in each neuronal layer are driven by the waves in previous layers being naturally coherent in-phase [45]. In this regard, a recent paper has proposed that some chimeric states in neuronal networks may explain synchronization between different areas by bioelectromagnetic field coupling [79]. In nonlinear dynamics, a chimera state is the spatial concurrence of coherent (synchronous) and incoherent (nonsynchronous) dynamical behavior that arises in a network of oscillators [79].…”

“…In this regard, a recent paper has proposed that some chimeric states in neuronal networks may explain synchronization between different areas by bioelectromagnetic field coupling [79]. In nonlinear dynamics, a chimera state is the spatial concurrence of coherent (synchronous) and incoherent (nonsynchronous) dynamical behavior that arises in a network of oscillators [79]. This recent approach suggests that magnetic flux across the membrane of neurons can effectively act as a supplementary mode of information exchange, supporting the idea that alternating chimera patterns can emerge in a network of neuronal systems coupled through electromagnetic fields [79].…”

Chimera patterns in three-dimensional locally coupled systems

“…The existence of chimera states is also detected in two interacting different populations where each oscillator in each population interacts in nonlocal [49] and global fashion [50]. Recently, the emergence of alternating chimera in a network of identical neuronal systems induced by an external electromagnetic field has been reported in [51]. Depending on the spatiotemporal motion of the oscillators in the network, different types of non-stationary chimera patterns are categorized which include imperfect chimera [52], travelling chimera [53], imperfect travelling chimera [54], and spiral wave chimera states [55,56].…”