Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra compet...

• Author(s): Costa, Fernando Pestana da ; Pinto, João Teixeira ; Sasportes, Rafael ; Roessel, Henry J. van
• Date: 2012
• Persistent ID: http://hdl.handle.net/10400.2/2124
• Origin: Repositório Aberto da Universidade Aberta
• Subject(s): Equações de coagulação-aniquilação; Soluções Auto-semelhantes; Equações de Lotka-Volterra
• Document Type: Article
• Language: English

Description

In a recent paper, Laurencot and van Roessel (2010 J. Phys. A: Math. Theor., 43, 455210) studied the scaling behaviour of solutions to a two-species coagulation–annihilation system with total annihilation and equal strength coagulation, and identified cases where self-similar behaviour occurs, and others where it does not. In this paper, we proceed with the study of this kind of system by assuming that the coagulation rates of the two different species need not be equal. By applying Laplace transform techniques, the problem is transformed into a two-dimensional ordinary differential system that can be transformed into a Lotka–Volterra competition model. The long-time behaviour of solutions to this Lotka–Volterra system helps explain the different cases of existence and nonexistence of similarity behaviour, as well as why, in some cases, the behaviour is nonuniversal, in the sense of being dependent on initial conditions.