Kolmogorov Vector Fields with Robustly Permanent Subsystems |
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Authors: | Janusz MierczyńskiSebastian J Schreiber |
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Institution: | a Institute of Mathematics, Wroc?aw University of Technology, Wybrzeze Wyspiańskiego 27, PL-50-370, Wroc?aw, Polandf1mierczyn@im.pwr.wroc.plf1b Department of Mathematics, Western Washington University, Bellingham, Washington, 98225, f2sschreib@cc.wwu.eduf2 |
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Abstract: | The following results are proven. All subsystems of a dissipative Kolmogorov vector field ?i = xifi(x) are robustly permanent if and only if the external Lyapunov exponents are positive for every ergodic probability measure μ with support in the boundary of the nonnegative orthant. If the vector field is also totally competitive, its carrying simplex is C1. Applying these results to dissipative Lotka-Volterra systems, robust permanence of all subsystems is equivalent to every equilibrium x* satisfying fi(x* > 0 whenever xi* = 0. If in addition the Lotka-Volterra system is totally competitive, then its carrying simplex is C1. |
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