Emergence of chaos in starlike networks of dissipative nonlinear oscillators by localized parametric excitations.

We study the effectiveness of locally controlling the impulse transmitted by parametric periodic excitations at inducing and suppressing chaos in starlike networks of driven damped pendula, leading to asynchronous chaotic states and equilibria, respectively. We found that the inducing (suppressor) effect of increasing (decreasing) the impulse transmitted by the parametric excitations acting on particular nodes depends strongly on their number and degree of connectivity as well as the coupling strength. Additionally, we provide a theoretical analysis explaining the basic physical mechanisms of the emergence and suppression of chaos as well as the main features of the chaos-control scenario. Our findings constitute proof of the impulse-induced control of chaos in a simple model of complex networks, thus opening the way to its application to real-world networks.