Controlling chimera and solitary states by additive noise in networks of chaotic maps

Abstract

We study numerically the spatio-temporal dynamics of ring networks of coupled discrete-time systems in the presence of additive noise. The robustness of chimera states with respect to noise perturbations is explored for two ensembles in which the individual elements are described by either logistic maps or Henon maps in the chaotic regime. The influence of noise on the behavior of solitary states is investigated for a ring of nonlocally coupled Lozi maps. Numerical simulations are performed for a set of different noise realizations and random initial conditions to provide reliable statistical data. The type of dynamics of the considered networks is quantified by using a cross-correlation coefficient. We find that there is a finite and sufficiently wide region with respect to the coupling strength and the noise intensity where the probability of observing the chimeras and solitary states is high.

Keywords:

• Nonlocal coupling
• chimera states
• solitary states
• logistic map
• Henon map
• Lozi map

2020 Mathematics Subject Classification:

• 37C05

Disclosure statement

The authors declare that there is no potential conflict of interest.

Additional information

Funding

E.R. and G.S. acknowledge financial support from the Russian Science Foundation (project No. 20-12-00119) (numerical simulation of the dynamics of the Henon and Lozi map networks). E.S. acknowledges financial support from the German Science Foundation (DFG-Projektnummer 429685422 and 440145547) (numerical simulation of the dynamics of the logistic map network).