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Mathematical Analysis of Predator-Prey System in Biotic Population

Author: LiJunZuo
Tutor: LvXianRui
School: Jilin University
Course: Applied Mathematics
Keywords: Predator - Prey Model Stage structure Parental care Stability Persistent Dissipative
CLC: O175
Type: Master's thesis
Year: 2010
Downloads: 165
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Abstract


Ecosystem , biological predator-prey behavior is a common phenomenon since the predator-prey model of the last century, Volterra and Lotka research , many of the relevant aspects of the researchers of the model was improved in the original model on the basis of considering the delay, the functional response of the population age structure and parental care , and many other factors , and the stability of the model , the persistence and dissipation properties discussed in a detailed analysis , many important results in this article is a articles on the synthesis of the predator -prey model , introduce a single population with stage structure model of growth delay , as the time goes to infinity , the system is stable , it tends to be a non-trivial equilibrium point . predator with Stage structure of predator - prey model in each positive solutions satisfy certain conditions , the system is long-lasting . positive when the predator prey growth minus own mortality , prey stage structure of prey - is prey model is lasting . persistence analysis predator - prey model with stage structure and time delay to be seen by the number of predators must be enough predator population is persistent . proportion of dependency and the proliferation of predator - prey model only strictly positive globally asymptotically stable ω- cycle solution exists under certain conditions are met . discussion prey have different inherent growth Predator - Prey model stability of parental care : when the prey has an exponential inherent in the type of growth , a positive balance of stability only with the ratio of the minor predators mortality and adult mortality . minors predator mortality than adult small , balanced asymptotically stable , otherwise unstable . Logistic type inherent growth prey , predators birth coefficient is less than the maturity coefficient , the Predators will perish. estimate predator - prey model positive Solutions of parental care , given certain conditions under steady-state solution of the system (a / b, 0,0) is globally asymptotically stable in R 3 .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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