| Abstract: |
| Carrying simplices (CSs) are a powerful tool in the investigation of competitive systems of ordinary differential equations (ODEs), as well as their time-discrete counterparts (both give rise to dissipative dynamical systems). Roughly speaking, they are unordered invariant sets, Lipschitz homeomorphic to the standard probability simplex, and forming the joint boundary between the repulsion sets of the origin and the point at infinity.
We prove the existence and investigate properties of time-periodic family of CSs for totally competitive time-periodic systems of ODEs where the right-hand sides satisfy the Carath\`eodory-type conditions. We utilize an existence theory of CSs for retrotone time-discrete dynamical systems, developed earlier by us, where the CS is defined as the joint limit of monotone sequences of images of a given set.
This is a joint work with Stephen Baigent, UCL. |
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