Partial Synchronization of Diffusively Coupled Chua Systems: An Experimental Case Study

Abstract

In this paper partial synchronization of diffusively coupled Chua systems is presented. Partial synchronization is defined as the situation where some circuits synchronize with each other, while others do not. An experimental setup, consisting of maximal four Chua circuits operating in the double scroll regime, is used to show the existence of linear invariant manifolds corresponding to the partial synchronized state.

Semi-passivity and synchronization of diffusively coupled neuronal oscillators

“…A similar phenomena is encountered in networks of diffusively coupled Chua circuits, cf. [41]. The piecewise linear model of the Chua circuit is not semi-passive (the Chua attractor is not globally stable) and due to the interaction the trajectories of the systems can be driven outside the domain of attraction such that the solutions grow unbounded.…”

Semi-passivity and synchronization of neuronal oscillators

“…(see v.d. Steen and Nijmeijer (2006) for an example with diffusively coupled Chua systems.) However, semi-passivity of the systems in the diffusively coupled network guarantees bounded solutions.…”

Semi-passivity and synchronization of diffusively coupled neuronal oscillators

“…Definition 3.1 (Convergent systems). [5,23] Consider the system ż = q(z, w(t)), (41) where the external signal w(t) is taking values from a compact set W ⊂ R. The system (41) is called convergent if i. all solutions z(t) are well-defined for all t ∈ (−∞, +∞) and all initial conditions z(0), ii. there exists an unique globally asymptotically stable solution z w (t) on the interval t ∈ (−∞, +∞) from which it follows…”