Controlling the diffusionless Lorenz equations with periodic parametric perturbation

DOI10.1016/J.CAMWA.2009.07.058zbMath1189.34118OpenAlexW2009958707MaRDI QIDQ979814

Zhouchao Wei, Qi-Gui Yang

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.07.058

zbMATH Keywords

chaosperiodic orbitshomoclinic orbitsMelnikov methodcontrolled DLEperiodic parameter perturbation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Singular perturbations for ordinary differential equations (34E15) Chaos control for problems involving ordinary differential equations (34H10)

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Cites Work

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• Adaptive control of chaos in Lorenz system
• Suppression of chaos through changes in the system variables: Transient chaos and crises
• Design of sliding mode controller for Lorenz chaotic system with nonlinear input
• The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Periodic orbits and homoclinic orbits of the diffusionless Lorenz equations
• A stable-manifold-based method for chaos control and synchronization
• Nonlinear feedback control of Lorenz system
• Controlling chaos with periodic parametric perturbations in Lorenz system
• New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High r in the Lorenz Equations
• Periodic Orbits in Slowly Varying Oscillators
• Homoclinic Orbits in Slowly Varying Oscillators
• SUPPRESSION OF CHAOS THROUGH CHANGES IN THE SYSTEM VARIABLES THROUGH POINCARÉ AND LORENZ RETURN MAPS
• Controlling Chaos Using Input–Output Linearization Approach

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