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Asymptotic synchronization in lattices of coupled nonidentical Lorenz equations. (English) Zbl 0983.37018
Summary: We study coupled nonidentical Lorenz equations with three different boundary conditions. Coupling rules and boundary conditions play essential roles in the qualitative analysis of solutions of coupled systems. By using Lyapunov stability theory, a sufficient condition is obtained for the global stability of trivial equilibrium of coupled system with Dirichlet condition. Then we restrict our attention on the dynamics of coupled nonidentical Lorenz equations with Neumann/periodic boundary condition and prove that the asymptotic synchronization occurs provided the coupling strengths are sufficiently large. That is, the difference between any two components of solution is bounded by the quantity $O( \varepsilon/ \max\{c_1, c_2,c_3\})$ as $t\to\infty$, where $\varepsilon$ is the maximal deviation of parameters of nonidentical Lorenz equations, and $c_1$, $c_2$ and $c_3$ are the specified coupling strengths.

37C25Fixed points, periodic points, fixed-point index theory
37C75Stability theory
37D45Strange attractors, chaotic dynamics
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