Systems of Coupled Piecewise-Linear Maps with Central Element: Stability of a Synchronized State

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We investigate the stability of a synchronized state in systems of coupled one-dimensional piecewise-linear maps that, by construction, contain a central element, i.e., an element that interacts with every other (peripheral) element of the system. Two types of systems are considered, namely, systems with and without interaction between peripheral elements. We establish conditions for the strong and weak stability of a synchronized state in systems considered.