Opera Medica et Physiologica

Traveling Chimera Pattern in a Neuronal Network under Local Gap Junctional and Nonlocal Chemical Synaptic Interactions

Author Affiliations

Arindam Mishra1,2*, Suman Saha2, 3, Dibakar Ghosh5, Gregory V. Osipov6, Syamal K. Dana2,4 

1 Department of Physics, Jadavpur University, Jadavpur, Kolkata 700032, India;
2 Center for Complex System Research Kolkata, Kolkata 700094, India;
3 Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata 700098, India;
4 CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India;
5 Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India;
6 Department of Control Theory, Nizhni Novgorod State University, Gagarin Avenue 23, 606950, Nizhni Novgorod, Russia.

Corresponding author: 

Arindam Mishra (arindammishra@gmail.com)

Syamal K. Dana (syamaldana@gmail.com)


A spatially stable pattern of two coexisting coherent and incoherent subpopulations in nonlocally coupled dynamical systems is called as chimera states and seen in many paradigmatic limit cycle as well as chaotic models where the coupling interaction is basically diffusive type. In neuronal networks, besides diffusive electrotonic communication via gap junctions, chemical transmission occurs between the pre-synapse and post-synapse of neurons. We consider, in a numerical study, a network of neurons in a ring using the Hindmarsh-Rose (HR) bursting model for each node of the network and, apply attractive gap junctions for local coupling between the nearest neighbors and inhibitory nonlocal coupling via chemical synaptic transmission between the distant neighbors. For a range of gap junctional and chemical synaptic coupling strengths, a subpopulation of the neuronal network, in the ring, bursts asynchronously and another subpopulation remains silent in a synchronous state. The bursting subpopulation of neurons fires sequentially along the ring when the number of firing nodes remains same but change their positions periodically in time. It appears as a traveling chimera pattern in the ring when the dynamics of the individual bursting nodes is chaotic. The chimera pattern travels in a reverse direction for a larger chemical synaptic coupling strength. A purely inhibitory chemical synaptic coupling can produce a similar traveling chimera pattern, however, the dynamics of the firing nodes is then periodic.