Matrix analysis
Relevance of dynamic clustering to biological networks
Proceedings of the NATO advanced research workshop and EGS topical workshop on Chaotic advection, tracer dynamics and turbulent dispersion
On contraction analysis for non-linear systems
Automatica (Journal of IFAC)
Partial synchronization and clustering in a system of diffusively coupled chaotic oscillators
Mathematics and Computers in Simulation
Stable concurrent synchronization in dynamic system networks
Neural Networks
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In this paper we investigate the problem of partial synchronization in diffusively coupled chemical chaotic oscillators with zero-flux boundary conditions. The dynamical properties of the chemical system which oscillates with Uniform Phase evolution, yet has Chaotic Amplitudes (UPCA) are first discussed. By combining numerical and analytical methods, the impossibility of full global synchronization in a network of two or three coupled chemical oscillators is discovered. Mathematically, stable partial synchronization corresponds to convergence to a linear invariant manifold of the global state space. The sufficient conditions for exponential stability of the invariant manifold in a network of three coupled chemical oscillators are obtained via the nonlinear contraction principle.