Robust cycles in Kolmogorov–Lotka–Volterra class of models with intraspecific co-operation. (December 2016)

• Record Type: Journal Article
• Authors: Datta, Soumya
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 98
• Page End: 110
• Publication Date: 2016-12
• Subjects: Kolmogorov–Lotka–Volterra model -- Predator–prey -- Social networks -- Andronov–Hopf bifurcation -- Limit cycles; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.04.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Using the Andronov–Hopf bifurcation theorem and the Poincaré–Bendixson Theorem, we explore robust cyclical possibilities in Kolmogorov–Lotka–Volterra class of models with positive intraspecific cooperation (in the form of social networks) in the prey population. We find that this additional feedback effect of intraspecific cooperation introduces nonlinearities which modify the cyclical outcomes of the model. We show that the cyclical outcomes are more robust than in the existing literature in this area due to introduction of such non-linearities. We also demonstrate the possibilities of multiple limit cycles under certain situations.