DYNAMICS AND BIFURCATIONS IN A TWO-PREYS ONE-PREDATOR SYSTEM WITH TWO TYPES OF RESPONSE FUNCTIONS

• Main Author: Marwan
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/41888
• Institution: Institut Teknologi Bandung

In this research, we consider the dynamics and bifurcations in a two-preys onepredator system. Unlike previous studies on similar model where the two-preys population generally consist of two different species, in this research we assume that the population of the prey is classified into two classes: the productive prey and the nonproductive prey. There are two important consequences of this assumption. First, the growth function of these classes will be influenced by a different factor. The productive prey population growth comes from their birth, while the nonproductive prey population comes from ’migration’ of the productive prey. Second, the response of predation which is modeled as response function also differs in each prey population class. We use response function of Holling II type for the productive prey, and for the nonproductive prey, we have response function of Holling IV type. The response function of Holling II accommodates saturation factor of predation, while the response function of Holling IV accommodates group defense mechanism. By using numerical continuation method we found some bifurcations of both equilibria and periodic solution. For the equilibria, we have observed the codimension one bifurcation, i.e.: fold, Hopf and transcritical. We also found three co-dimension two bifurcations, namely cusp, Bautin, and Bogdanov- Takens. For the bifurcation of the periodic solution, we have found the existence of fold of limit cycle, homoclinic and period-doubling bifurcation respectively. A dynamic called infinitely many equilibria was also founded in a subsystem of the two-preys one-predator system. In addition, we propose an alternative method on computing the fold bifurcation point by applying the Lagrange multiplier method.