PREDATOR-PREY MODELS WITH COMPETITION, PART III: CLASSIFICATION OF STATIONARY SOLUTIONS

Henri Berestycki (1) , Alessandro Zilio (2)

1 CAMS - Centre d'Analyse et de Mathématique sociales
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

For a stationary system representing prey and N groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if the number of components N is too large or if the competition between different groups is too small, then the system has only constant solutions, which we then completely characterize.

Domaines: Equations aux dérivées partielles [math.AP]

Henri Berestycki, Alessandro Zilio. PREDATOR-PREY MODELS WITH COMPETITION, PART III: CLASSIFICATION OF STATIONARY SOLUTIONS. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12), pp.7141-7162. ⟨10.3934/dcds.2019299⟩. ⟨hal-03884852⟩