Analytical and numerical investigation of two families of Lorenz-like dynamical systems

DOI10.1016/j.chaos.2006.03.037zbMath1130.37018OpenAlexW2014649508MaRDI QIDQ2468246

T. Spassova, Nikolay K. Vitanov, S. Panchev

Publication date: 30 January 2008

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2006.03.037

zbMATH Keywords

stabilityfixed pointsLyapunov exponentschaotic attractorsLyapunov dimensiongeneralized Lorenz systemBurke-Shaw system

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

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Uses Software

• Dynamics

Cites Work

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• Chaos control in Duffing system
• A new reduced-order observer design for the synchronization of Lorenz systems
• On the relation between Rayleigh-Bénard convection and Lorenz system
• Chaotic pairwise competition
• Influence of adaptation on the nonlinear dynamics of a system of competing populations
• The Lyapunov dimension of strange attractors
• Dynamics: numerical explorations. Accompanying computer program dynamics. Coauthored by Eric J. Kostelich. With 3 1/2 DOS Diskette
• Nonlinear dynamics and chaos control for a time delay Duffing system
• The Lorenz equations: bifurcations, chaos, and strange attractors
• The extended Malkus-Robbins dynamo as a perturbed Lorenz system
• Dynamical consequences of adaptation of the growth rates in a system of three competing populations
• Evolution of a multimodal map induced by an equivariant vector field
• Deterministic Nonperiodic Flow
• FREQUENCY DOMAIN METHOD FOR THE DICHOTOMY OF MODIFIED CHUA'S EQUATIONS
• Adaptation and its impact on the dynamics of a system of three competing populations