Engineering chimera patterns in networks using heterogeneous delays

Basin of attraction for chimera states in a network of Rössler oscillators

Chimera states are spatiotemporal patterns in which coherent and incoherent dynamics coexist simultaneously. These patterns were observed in both locally and nonlocally coupled oscillators. We study the existence of chimera states in networks of coupled Rössler oscillators. The Rössler oscillator can exhibit periodic or chaotic behavior depending on the control parameters. In this work, we show that the existence of coherent, incoherent, and chimera states depends not only on the coupling strength, but also on the initial state of the network. The initial states can belong to complex basins of attraction that are not homogeneously distributed. Due to this fact, we characterize the basins by means of the uncertainty exponent and basin stability. In our simulations, we find basin boundaries with smooth, fractal, and riddled structures.

Spike chimera states and firing regularities in neuronal hypernetworks

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.