TAILIEUCHUNG - Equilibria in a dipersal model for structured populations

We derive a model for structured population with a two-phase life cycle. Growth and reproduction occur during the first phase. The first phase is followed by a dispersal phase in which individuals are allowed to move throughout a habitat. Also, we prove the existence of a branch of positive equilibria using bifurcation results of Rabinowitz. | Turk J Math 31 (2007) , 421 – 433. ¨ ITAK ˙ c TUB Equilibria in a Dipersal Model for Structured Populations Maref Y. M. Alzoubi Abstract We derive a model for structured population with a two-phase life cycle. Growth and reproduction occur during the first phase. The first phase is followed by a dispersal phase in which individuals are allowed to move throughout a habitat. Also, we prove the existence of a branch of positive equilibria using bifurcation results of Rabinowitz. Key Words: Integro-difference equations, Dynamical systems, Dispersion, Structured populations. 1. Introduction Dispersal within a population is one of the most notable characteristics of individuals. Individuals move in their habitat for several reasons, including crowding, environmental fluctuations, diseases, etc., and this movement can greatly affect the dynamics of the population. Therefore, it is important to take dispersal into account when studying stability and persistence of populations. Dispersal was incorporated into population models in the pioneering work of Skellam [22], Kierstead and Slobodking [10], Fisher [5], Kolmogrov, Petrovsky and Piscounov [9]. Also, dispersal occurs in studies by Levin [14], McMurtrie [18], Cohen and Murray [3], Hamilton and May [6], MacArthur and Wilson [17], Levin and Segel [16], Vance [23], Ellner [4], Liven, Cohen, and Hastings [15], and Okubo [19]. 2000 AMS Mathematics Subject Classification: 93D99, 93C10, 93B18, 93A30. 421 ALZOUBI In the earlier studies of dispersal there was an emphasis on continuous time growth models based on reaction-diffusion equations. However, the cycle of many populations involves two phases. The year of these populations is divided into two distinct stages: the growth phase, in which the population grows and produces newborns and a dispersal phase, in which the newborns disperse. Examples of such populations include annual plants and many insects. Such life cycle characteristics motivated Kot and Schaffer [11] to model

• Toán học
• Integro difference equations
• Dynamical systems
• Structured populations
• Dipersal model
• Two phase life cycle