A complex spatiotemporal pattern with coexisting coherent and incoherent domains in a network of identically coupled oscillators is known as a chimera state. Here, we report the emergence and existence of a novel type of nonstationary chimera pattern in a network of identically coupled Hindmarsh–Rose neuronal oscillators in the presence of synaptic couplings. The development of brain function is mainly dependent on the interneuronal communications via bidirectional electrical gap junctions and unidirectional chemical synapses. In our study, we first consider a network of nonlocally coupled neurons where the interactions occur through chemical synapses. We uncover a new type of spatiotemporal pattern, which we call “spike chimera” induced by the desynchronized spikes of the coupled neurons with the coherent quiescent state. Thereafter, imperfect traveling chimera states emerge in a neuronal hypernetwork (which is characterized by the simultaneous presence of electrical and chemical synapses). Using suitable characterizations, such as local order parameter, strength of incoherence, and velocity profile, the existence of several dynamical states together with chimera states is identified in a wide range of parameter space. We also investigate the robustness of these nonstationary chimera states together with incoherent, coherent, and resting states with respect to initial conditions by using the basin stability measurement. Finally, we extend our study for the effect of firing regularity in the observed states. Interestingly, we find that the coherent motion of the neuronal network promotes the entire system to regular firing.
Skip Nav Destination
,
,
,
Article navigation
Research Article|
May 20 2019
Spike chimera states and firing regularities in neuronal hypernetworks
Bidesh K. Bera;
Bidesh K. Bera
1
Department of Mathematics, Indian Institute of Technology Ropar
, Punjab 140001, India
2
Physics and Applied Mathematics Unit, Indian Statistical Institute
, 203 B.T. Road, Kolkata 700108, India
Search for other works by this author on:
Sarbendu Rakshit;
Sarbendu Rakshit
2
Physics and Applied Mathematics Unit, Indian Statistical Institute
, 203 B.T. Road, Kolkata 700108, India
Search for other works by this author on:
Dibakar Ghosh
;
Dibakar Ghosh
a)
2
Physics and Applied Mathematics Unit, Indian Statistical Institute
, 203 B.T. Road, Kolkata 700108, India
Search for other works by this author on:
Jürgen Kurths
Jürgen Kurths
3
Potsdam Institute for Climate Impact Research
, Potsdam 14473, Germany
4
Saratov State University
, Saratov 4410012, Russia
Search for other works by this author on:
Bidesh K. Bera
1,2
Sarbendu Rakshit
2
Dibakar Ghosh
2,a)
Jürgen Kurths
3,4
1
Department of Mathematics, Indian Institute of Technology Ropar
, Punjab 140001, India
2
Physics and Applied Mathematics Unit, Indian Statistical Institute
, 203 B.T. Road, Kolkata 700108, India
3
Potsdam Institute for Climate Impact Research
, Potsdam 14473, Germany
4
Saratov State University
, Saratov 4410012, Russia
a)
Electronic mail: [email protected]
Note: This paper is part of the Focus Issue, “Nonlinear Chemical Dynamics and Its Interdisciplinary Impact: Dedicated to Ken Showalter on the Occasion of his 70th Birthday”.
Chaos 29, 053115 (2019)
Article history
Received:
January 09 2019
Accepted:
April 24 2019
Citation
Bidesh K. Bera, Sarbendu Rakshit, Dibakar Ghosh, Jürgen Kurths; Spike chimera states and firing regularities in neuronal hypernetworks. Chaos 1 May 2019; 29 (5): 053115. https://doi.org/10.1063/1.5088833
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Introduction to Focus Issue: Data-driven models and analysis of complex systems
Johann H. Martínez, Klaus Lehnertz, et al.
Reservoir computing with the minimum description length principle
Antony Mizzi, Michael Small, et al.
Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology
Eugene Tan, Shannon Algar, et al.
Related Content
Brand effect versus competitiveness in hypernetworks
Chaos (February 2015)
A hyper-distance-based method for hypernetwork comparison
Chaos (August 2024)
Multistability and evolution of chimera states in a network of type II Morris–Lecar neurons with asymmetrical nonlocal inhibitory connections
Chaos (October 2022)
Dynamical evolution behavior of scientific collaboration hypernetwork
AIP Advances (November 2022)