Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India.
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India.
Chaos. 2019 May;29(5):053115. doi: 10.1063/1.5088833.
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.
在相同耦合振荡器的网络中，共存相干和非相干区域的复杂时空模式被称为嵌同态。在这里，我们报告了在存在突触耦合的相同耦合 Hindmarsh-Rose 神经元振荡器网络中出现并存在一种新型非稳态嵌同模式。大脑功能的发展主要依赖于通过双向电间隙连接和单向化学突触的神经元间通讯。在我们的研究中，我们首先考虑通过化学突触发生相互作用的非局部耦合神经元网络。我们揭示了一种新的时空模式，我们称之为“由耦合神经元的去同步脉冲引起的尖峰嵌同”，具有相干静止状态。此后，在神经元超网络中出现了不完善的行波嵌同状态（其特征是同时存在电和化学突触）。使用适当的特征，如局部序参量、非相干强度和速度分布，可以在广泛的参数空间中识别出几种动态状态以及嵌同状态。我们还通过使用基区稳定性测量来研究这些非稳态嵌同状态以及非相干、相干和静止状态对初始条件的鲁棒性。最后，我们将研究扩展到观察到的状态中的点火规则性的影响。有趣的是，我们发现神经元网络的相干运动促进了整个系统的规则点火。
