A product theorem for connection matrices and the structure of connecting orbits

DOI10.1016/0362-546X(94)90148-1zbMath0818.34024OpenAlexW1995311900MaRDI QIDQ4322174

Konstantin Mischaikow, James F. Reineck

Publication date: 22 August 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)90148-1

zbMATH Keywords

Conley indexMorse decompositionpredator-prey systemconnecting orbitsconnection matrixflow on a locally compact space

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Nonlinear differential equations in abstract spaces (34G20) Dynamics induced by flows and semiflows (37C10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

The connection matrix and heteroclinic cycles in two prey-predator pairs with multiple equilibria

Cites Work

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• On the existence of intermediate magnetohydrodynamic shock waves
• Connecting orbits in scalar reaction diffusion equations. II: The complete solution
• Morse decompositions for delay-differential equations
• The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces
• A dynamical system approach to a phase transition problem
• Dynamics of bifurcations for variational problems with \(O(3)\) equivariance: A Conley index approach
• Index Filtrations and the Homology Index Braid for Partially Ordered Morse Decompositions
• The Connection Matrix Theory for Morse Decompositions
• The Continuation Theory for Morse Decompositions and Connection Matrices
• Connected Simple Systems and The Conley Index of Isolated Invariant Sets
• A refinement of the Conley index and an application to the stability of hyperbolic invariant sets
• The Connection Map for Attractor-Repeller Pairs
• Existence of Generalized Homoclinic Orbits for one Parameter Families of Flows
• Connecting orbits in one-parameter families of flows
• Transition systems
• A connection matrix analysis of ecological models
• Algebraic transition matrices in the Conley index theory
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

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