Author pages are created from data sourced from our academic publisher partnerships and public sources.

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

2,792 106

Convergent activation dynamics in continuous time networks

- M. Hirsch
- Mathematics, Computer Science
- Neural Networks
- 1 July 1989

TLDR

588 39- PDF

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

928 36- PDF

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

344 34

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

478 29

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

419 27

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

369 26- PDF

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

178 18

...

1

2

3

4

5

...