DCDS
Cooperative random and stochastic differential equations
Ludwig Arnold Igor Chueshov
Discrete & Continuous Dynamical Systems - A 2001, 7(1): 1-33 doi: 10.3934/dcds.2001.7.1
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
Discrete & Continuous Dynamical Systems - B 2018, 23(3): ⅰ-ⅸ doi: 10.3934/dcdsb.201803i
keywords: Ship stability determining functional inertial manifold monotone random systems quasi-stability synchronization for stochastic systems

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