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Full-Text Articles in Non-linear Dynamics
Dynamics Of Prey-Prey Mutualism With Varying Carrying Capacity And Herd Behavior In The Presence Of Predator, Felix Dela Djokoto
Dynamics Of Prey-Prey Mutualism With Varying Carrying Capacity And Herd Behavior In The Presence Of Predator, Felix Dela Djokoto
UNF Graduate Theses and Dissertations
This study investigates the dynamics of mutualistic relationships between two prey species in the presence of a predator, by taking into account herding in one species along with the influence of carrying capacities between two prey species. These mutualistic dynamics are presented by constructing two mathematical models, namely an indirect and direct mutualism model. As the strength of the symbiotic relationship increases the indirect model goes through transcritical bifurcation to Hopf bifurcation whereas in the direct mutualism model goes through saddle-node bifurcation to Hopf bifurcation.
Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona
Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona
Honors Undergraduate Theses
Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …
On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin
On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin
Graduate Theses/Dissertations
In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.
A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark
A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark
Theses and Dissertations
This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.