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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,
Convergent activation dynamics in continuous time networks
  • M. Hirsch
  • Mathematics, Computer Science
    Neural Networks
  • 1 July 1989
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 le
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).
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
Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games
Abstract Fictitious play in infinitely repeated, randomly perturbed games is investigated. Dynamical systems theory is used to study the Markov process { x k }, whose state vector x k lists the
Systems of Differential Equations that are Competitive or Cooperative
A drive nut is mounted at one end of a load distributing carriage through which passes a threaded shaft which is fixed against rotation and engaged with said nut. The nut is rotationally driven about