Abstract
The attractive coupling, in combination with the repulsive coupling, plays a significant role in eliciting a variety of collective dynamical behaviors. Due to its importance, we present a brief outline of the consequences of repulsive coupling in coupled nonlinear oscillators. Significantly, by incorporating control parameters in the repulsive coupling alone, we analyze the effect of repulsive coupling on collective dynamical behavior. Such parameters greatly control the efficiency of repulsive coupling, which results in the observation of various dynamical transitions. For instance, we find that the transition from traveling wave (TW) to synchronized (SYN) state through imperfect traveling chimera (ITC) state while reducing the control parameter from the maximal value at the traveling wave. Similarly, the transition to the synchronized state is observed through cluster chimera death (CCD), cluster oscillation death (COD), and imperfect amplitude chimera (IAC) states by decreasing the control parameter at the multi-chimera death (MCD) state. Specifically, we find that the observed collective dynamical behaviors including TW, ITC, IAC, CCD, COD, and MCD exist as consequences of the strength of repulsive coupling and nonlocal interactions. Finally, the perseverance of imperfect chimera states is also investigated in the presence of additional noise.