منابع مشابه
Robust Permanence for Ecological Maps
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...
متن کاملRobust permanence for ecological equations with internal and external feedbacks.
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...
متن کاملRobust Permanence for Ecological Differential Equations, Minimax, and Discretizations
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...
متن کاملRobust Permanence for Ecological Maps | SIAM Journal on Mathematical Analysis | Vol. 49, No. 5 | Society for Industrial and Applied Mathematics
We consider ecological difference equations of the form xt+1 = x i tAi(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 = (xt , x 2 t , . . . , x m t ) is the state of the entire community, and Ai(xt) are matrices determining the update rule for species i. These equations are pe...
متن کاملCriteria 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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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2017
ISSN: 0036-1410,1095-7154
DOI: 10.1137/16m1066440