In-phase and anti-phase bursting dynamics and synchronisation scenario in neural network by varying coupling phase

We have analysed the phase flip in the membrane potential and the subsequent emergence of patterns in a network of Hindmarsh Rose neurons under the influence of self, mixed and cross coupling of state variables. The interactions are realised using rotation matrix and the toggle among self, mixed and cross coupling modes are carried out by varying the coupling phase. With the increase in number of variables having self coupling, the value of coupling strength at which synchrony is obtained, decreases drastically. The activator self or cross coupling in membrane potential induces in-phase synchrony whereas the inhibitor coupling induces anti-phase bursts. Due to the interplay of non local coupling and rotation symmetry breaking by crosscoupling of state variables, chimera, multi chimera and traveling chimera states are obtained in the N coupled network. We found that self coupling in multiple variables itself could induce symmetry break in the network proving that cross coupling is not a prerequisite for obtaining chimera. The strength of incoherence and discontinuity measure validates the existence of chimera and multichimera states. The inhibitor self coupling in local interaction induces interesting patterns like Mixed Oscillatory State and clusters. This study of the transition mechanism between in-phase and anti-phase oscillations may help in understanding the realistic spatiotemporal communications of brain. PACS 05.45.-a · 05.45.Xt