Criteria for stochastic pinning control of networks of chaotic maps.
This paper investigates the controllability of discrete-time networks of coupled chaotic maps through stochastic pinning. In this control scheme, the network dynamics are steered towards a desired trajectory through a feedback control input that is applied stochastically to the network nodes. The network controllability is studied by analyzing the local mean square stability of the error dynamics with respect to the desired trajectory. Through the analysis of the spectral properties of salient matrices, a toolbox of conditions for controllability are obtained, in terms of the dynamics of the individual maps, algebraic properties of the network, and the probability distribution of the pinning control. We demonstrate the use of these conditions in the design of a stochastic pinning control strategy for networks of Chirikov standard maps. To elucidate the applicability of the approach, we consider different network topologies and compare five different stochastic pinning strategies through extensive numerical simulations.
Department of Mechanical and Aerospace Engineering, Polytechnic School of Engineering, New York University, Brooklyn, New York 11201, USA.
Violet
V
Mwaffo
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples 80125, Italy.
Pietro
P
DeLellis
Department of Mechanical and Aerospace Engineering, Polytechnic School of Engineering, New York University, Brooklyn, New York 11201, USA.
Maurizio
M
Porfiri