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- Publications
- Influence
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
- 707
- 112
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 the… Expand
Convergent activation dynamics in continuous time networks
- M. Hirsch
- Mathematics, Computer Science
- Neural Networks
- 1 July 1989
TLDR
Differential Equations, Dynamical Systems, and an Introduction to Chaos
- M. Hirsch, S. Smale, R. Devaney
- Mathematics
- 2003
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 level… Expand
Stability and convergence in strongly monotone dynamical systems.
- M. Hirsch
- Mathematics
- 1988
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 le… Expand
Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
- M. Hirsch
- Mathematics
- 1 May 1985
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
Immersions of manifolds
- M. Hirsch
- Mathematics
- 1 February 1959
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
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 point… Expand
Chain Transitivity, Attractivity, and Strong Repellors for Semidynamical Systems
- M. Hirsch, H. Smith, Xiao-qiang Zhao
- Mathematics
- 2001
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, and… Expand
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