Kolmogorov Vector Fields with Robustly Permanent Subsystems
✍ Scribed by Janusz Mierczyński; Sebastian J. Schreiber
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 97 KB
- Volume
- 267
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
The following results are proven. All subsystems of a dissipative Kolmogorov vector field ẋi = x i f i 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 C 1 . Applying these results to dissipative Lotka-Volterra systems, robust permanence of all subsystems is equivalent to every equilibrium x * satisfying f i x * > 0 whenever x * i = 0. If in addition the Lotka-Volterra system is totally competitive, then its carrying simplex is C 1 . 2002 Elsevier Science (USA)