Dynamics Of The Adaptive Growth Of A Single Species In An Environment With An Exponential Growth Resource

Population dynamics is one of the most important and systematic fields of biomathematics. It studies the growth conditions of species and the relationship between the species and the environment. One single species dynamic models are the most important population dynamic models. They study the growth dynamics of a single species by assuming different parameters to represent the effects of the environment. One single species dynamic models reflect the essence of population growth and are the basic of biomathematics.In this study, we studied two different growth dynamics of a single species in environment with an exponential growth resource. The thesis consists three chapters.In Chapter 1, we introduced the development of the studies of population dynamics and some single species dynamic models.In Chapter 2, we established the basic equations of (2.1) and (2.2) describing the growth of a single species in environment with an exponential growth resource as follows,By assumingμB is a constant, we obtained the exact solution of the model, proved that, both the species and the resource will increase if and only if the following condition meets, 0≤μ<r0,S0≥(αμB+β)/(r0-μ)X0, and studied the growth dynamics of the species and resource under different initial conditions.In Chapter 3, we suggested the concept of adaptive growth based on the fact of ratio-dependent growth. By introducing a new variable of Y and assuming Y follows the exponential growth law, we established the adaptive exponential growth model of (3.2) and (3.3), Based on the obtained exact solution of the model, we discussed the adaptive growth dynamics and proved that both the species and the resource will decrease with an exponential adaptive growth.Chapter 4 follows the work of Chapter 3. By assuming Y follows the logistic growth law, we established the adaptive logistic growth model of (4.2) and (4.3), Based on the obtained exact solution of the model, we discussed the adaptive growth dynamics and proved that both the species and the resource will increase with the same exponential rate if r0-(αμD+β) Ym> 0.