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4. Monotone Dynamical Systems
This chapter surveys a restricted but useful class of dynamical systems, namely, those enjoying a comparisonprinciple with respect to a closed order relation on the state space.Such systems,Expand
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Differential Equations, Dynamical Systems, and Linear Algebra
This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by theExpand
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Convergent activation dynamics in continuous time networks
  • M. Hirsch
  • Mathematics, Computer Science
  • Neural Networks
  • 1 July 1989
The activation dynamics of nets are considered from a rigorous mathematical point of view. Expand
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Differential Equations, Dynamical Systems, and an Introduction to Chaos
Hirsch, Devaney, and Smale's classic "Differential Equations, Dynamical Systems, and an Introduction to Chaos" has been used by professors as the primary text for undergraduate and graduate levelExpand
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Stability and convergence in strongly monotone dynamical systems.
Soit (X, Φ) un systeme dynamique: X est un espace topologique et le flot Φ={Φ t } t∈R+ est une famille d'applications continues de sous-ensembles ouverts de X dans X. On decrit qualitativement leExpand
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Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative).Expand
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Immersions of manifolds
Immersions of an m-manifold in an n-manifold, n>m, are classified up to regular homotopy by the homotopy classes of sections of a vector bundle E associated to the tangent bundle of M.  When N = Rn ,Expand
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Stable manifolds for hyperbolic sets
turns out that they STABLE MANIFOLDS AND HYPERBOLIC SETS ' MORRIS W. I-{HIRSCH AND CHARLES c. PUGH - 0. Introduction. Let U be an open set in a smooth manifold M and f '.U —» M a C‘ map. A fixed pointExpand
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Chain Transitivity, Attractivity, and Strong Repellors for Semidynamical Systems
Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, andExpand
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