Evaluation of the largest Lyapunov exponent in dynamical systems with time delay. (English) Zbl 1071.37014
Summary: A method of estimation of the largest Lyapunov exponents for dynamical systems with time delay is developed. This method can be applied both for flows and discrete maps. Our approach is based on the phenomenon of synchronization of identical systems coupled by linear negative feedback mechanism (flows) and exponential perturbation (maps). The existence of linear dependence of the largest Lyapunov exponent on the coupled parameter allows a precise estimation on this exponent.
MSC:
| 37C10 | Dynamics induced by flows and semiflows |
| 34K20 | Stability theory of functional-differential equations |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93D15 | Stabilization of systems by feedback |
Keywords:
chaotic systems; feedback control; dynamical systems with time delay; synchronization; identical systems; Lyapunov exponent; coupled parameterSoftware:
DynamicsReferences:
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