منابع مشابه
Criteria for C Robust Permanence
Let x* i=xi fi (x) (i=1, ..., n) be a C r vector field that generates a dissipative flow , on the positive cone of R. , is called permanent if the boundary of the positive cone is repelling. , is called C r robustly permanent if , remains permanent for sufficiently small C r perturbations of the vector field. A necessary condition and a sufficient condition for C r robust permanence involving t...
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We consider ecological difference equations of the form X i t+1 = X i t Ai(Xt) where X i t is a vector of densities corresponding to the subpopulations of species i (e.g. subpopulations of different ages or living in different patches), Xt = (X 1 t , X 2 t ,. .. , X m t) is state of the entire community, and Ai(Xt) are matrices determining the update rule for species i. These equations are perm...
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The dynamics of interacting structured populations can be modeled by dxi dt = Ai(x)xi where xi ∈ R ni , x = (x1, . . . , xk), and Ai(x) are matrices with non-negative off-diagonal entries. These models are permanent if there exists a positive global attractor and are robustly permanent if they remain permanent following perturbations of Ai(x). Necessary and sufficient conditions for robust perm...
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Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecologica...
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We present a sufficient condition for robust permanence of ecological (or Kolmogorov) differential equations based on average Liapunov functions. Via the minimax theorem we rederive Schreiber’s sufficient condition [S. Schreiber, J. Differential Equations, 162 (2000), pp. 400–426] in terms of Liapunov exponents and give various generalizations. Then we study robustness of permanence criteria ag...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2000
ISSN: 0022-0396
DOI: 10.1006/jdeq.1999.3719