Power spectra and dynamical invariants for delay-differential and difference equations

DOI10.1016/S0167-2789(97)00185-1zbMath0935.34062OpenAlexW2044676553MaRDI QIDQ1963415

Boualem Mensour, André Longtin

Publication date: 1 February 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(97)00185-1

zbMATH Keywords

feedback systemsattractorpower spectraLyapunov dimensionpositive Lyapunov exponentsdelay-differential and difference equationsMackey-Glass and Ikeda delay-differential equationsmode of oscillationnear-periodic superimposed modulation

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Stability theory of functional-differential equations (34K20) General spectral theory of ordinary differential operators (34L05) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Oscillation theory of functional-differential equations (34K11) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex (chaotic) behavior of solutions to functional-differential equations (34K23)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• High-dimensional chaotic behavior in systems with time-delayed feedback
• Chaotic attractors of an infinite-dimensional dynamical system
• Study of a high-dimensional chaotic attractor
• Discrete delay, distributed delay and stability switches
• High-dimensional chaos in delayed dynamical systems
• Exponential decay of power spectra at high frequency and positive Lyapunov exponents
• A Hopf-like equation and perturbation theory for differential delay equations
• Controlling chaos to store information in delay-differential equations
• Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Oscillation and Chaos in Physiological Control Systems

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