DCDS
Cooperative random and stochastic differential equations
Ludwig Arnold Igor Chueshov
This is a systematic study of order-preserving (or monotone) random dynamical systems which are generated by cooperative random or stochastic differential equations. Our main results concern the long-term behavior of these systems, in particular the existence of equilibria and attractors and a limit set trichotomy theorem. Several applications (models of the control of the protein synthesis in a cell, of gonorrhea infection and of symbiotic interaction in a random environment) are treated in detail.
keywords: order-preserving or monotone random dynamical system random attractor long-term behavior Cooperative differential equation random equilibrium limit set trichotomy.
DCDS-B
In memoriam igor d. chueshov september 23,1951 -april 23,2016
Ludwig Arnold
keywords: Ship stability determining functional inertial manifold monotone random systems quasi-stability synchronization for stochastic systems

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