Scaling properties of a hybrid Fermi-Ulam-bouncer model.
Singular strange attractors on the boundary of Morse-Smale systems
Sliding mode observers and observability singularity in chaotic synchronization.
Some numerical studies of dynamical systems
Some unresolved issued in non-linear population dynamics.
The Lyapunov exponent is a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions. Estimates of Lyapunov exponents are often used to characterize the qualitative population dynamics of insect time series. The methodology for estimation of the exponent for an observed, noisy, short ecological time series is still under development. Some progress has been made recently in providing measures of error for these exponents. Studies that do not account...
Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators.
Stabilizing the chaotic dynamics of the Lü system.
Stable and non-stable non-chaotic maps of the interval
Staircase baker's map generates flaring-type time series.
Statistical properties of unimodal maps
We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition...
Stochastic Stability in Some Chaotic Dynamical Systems.
Structural stability of Lorenz attractors
Structure of mappings of an interval with zero entropy
Sur un aspect numérique de la dimension fractale d'un attracteur chaotique
Symbolic dynamics and Lyapunov exponents for Lozi maps
Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.
Synchronization in ensembles of coupled maps with a major element.
Synchronization with error bound of non-identical forced oscillators
Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.
Synchronizing spatiotemporal chaos by introducing a finite flat region in the local map.
Synthesis of chaotic systems