Chaotic Motion Generated by Delayed Negative Feedback Part II: Construction of Nonlinearities

DOI10.1002/mana.3211800109zbMath0853.34065OpenAlexW2086576641MaRDI QIDQ4888020

Hans-Otto Walther, Bernhard Lani-Wayda

Publication date: 6 January 1997

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.3211800109

zbMATH Keywords

chaotic solutionsnegative feedbackdifferential delay equation

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (11)

Algorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation ⋮ Global dynamics of delay differential equations ⋮ Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations ⋮ Chaotic behavior in a class of delay difference equations ⋮ Change of the attractor structure for \(\dot x(t) = f(x(t-1)) \) when \(f\) changes from monotone to non-monotone negative feedback ⋮ On the floquet multipliers of periodic solutions to nonlinear functional differential equations ⋮ Chaos proved for a second-order difference differential equation ⋮ Stable periodic orbits for the Mackey-Glass equation ⋮ Periodic solutions for an \(N\)-dimensional cyclic feedback system with delay ⋮ Erratic solutions of simple delay equations ⋮ The Many Facets of Chaos

Cites Work

• Symbolic dynamics and nonlinear semiflows
• Existence of chaos in control systems with delayed feedback
• Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior)
• Chaotic motion generated by delayed negative feedback. I: A transversality criterion
• The stability of special symmetric solutions of with small amplitudes
• Homoclinic solution and chaos in
• The 2-dimensional attractor of 𝑥’(𝑡)=-𝜇𝑥(𝑡)+𝑓(𝑥(𝑡-1))
• Oscillation and Chaos in Physiological Control Systems
• Functional differential equations
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