Noninvertibility and the structure of basins of attraction in a model adaptive control system

DOI10.1007/BF01209149zbMath0798.93038MaRDI QIDQ1322669

Raymond A. Adomaitis, Ioannis G. Kevrekidis

Publication date: 5 May 1994

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

basins of attractionbasin structure

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Adaptive control/observation systems (93C40) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (16)

On noninvertible mappings of the plane: Eruptions ⋮ BIFURCATIONS OF STABLE SETS IN NONINVERTIBLE PLANAR MAPS ⋮ Some historical aspects of nonlinear dynamics -- possible trends for the future ⋮ BIFURCATIONS OF THE GLOBAL STABLE SET OF A PLANAR ENDOMORPHISM NEAR A CUSP SINGULARITY ⋮ A COMPUTER-ASSISTED STUDY OF GLOBAL DYNAMIC TRANSITIONS FOR A NONINVERTIBLE SYSTEM ⋮ On the boundaries of absorbing and chaotic areas in second-order endomorphisms ⋮ ABOUT A NEW CLASS OF INVARIANT AREAS GENERATED BY TWO-DIMENSIONAL ENDOMORPHISMS ⋮ Basin Properties in Two-Dimensional Noninvertible Maps ⋮ Chaos and fractal properties induced by noninvertibility of models in the form of maps ⋮ FRACTALIZATION OF BASIN BOUNDARY IN TWO-DIMENSIONAL NONINVERTIBLE MAPS ⋮ A METHOD TO CALCULATE BASIN BIFURCATION SETS FOR A TWO-DIMENSIONAL NONINVERTIBLE MAP ⋮ ON CRITICAL CURVES IN TWO-DIMENSIONAL ENDOMORPHISMS ⋮ Some Historical Aspects of Nonlinear Dynamics: Possible Trends for the Future ⋮ The Dynamics of Planar Quadratic Maps with Nonempty Bounded Critical Set ⋮ A route to computational chaos revisited: Noninvertibility and the breakup of an invariant circle ⋮ Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems

Uses Software

• AUTO
• AUTO-86

Cites Work

• Unnamed Item
• Nonlinear dynamics in adaptive control: Periodic and chaotic stabilization. II: Analysis
• Bifurcation in model reference adaptive control systems
• Recurrences and discrete dynamic systems
• Global bifurcations and chaos. Analytical methods
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Nonlinear dynamics in adaptive control: Chaotic and periodic stabilization

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