[PDF] Top 20 Control optimization and homoclinic bifurcation of a prey–predator model with ratio dependent

... pests. h ∈ [h 1 , h 2 ] represents the threshold of pests, where h 1 and h 2 are biological control level and chemical control level, respectively. K > 0 represents the environment carrying capacity of ... See full document

... the prey and predator ...called predator functional response) and q(z) satisfy the usual properties such as being nonnegative and increasing, and being equal to zero at ...following ... See full document

... ], ratio-dependent predator-prey models have received much attention from scientists (see, for example, ...following ratio-dependent predator-prey model ... See full document

... feedback control strategy [–]. The state feedback control is a threshold strategy which is used in impulsive semi-dynamic ...biological control method to control or eradicate the pest from ... See full document

... delayed ratio-dependent functional response predator-prey model with a threshold harvesting ...the model as well as boundedness and permanence properties are examined ...Hopf ... See full document

... the predator-prey model with prey-dependent Michaelis- Menten functional response exhibits is the so-called ”biolog- ical control paradox” [6], which states that we cannot have ... See full document

... delayed predator-prey system with Leslie-Gower and ratio-dependent Holling type III schemes subject to homogeneous Neumann boundary ...Hopf bifurcation induced by spatial diffusion and ... See full document

... eco-epidemiological model incorporating an prey refuge with disease in the prey population which is governed by modified logistic equation ...realistic model. A refuge can be important for the ... See full document

... and predator population known as Pelican birds, ...susceptible prey population den- sity and infected prey population density, respectively, at time t, and z represents predator population ... See full document

... a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are ... See full document

... transcritical bifurcation occurs. This local bifurcation leads to change the stability between two different equilibria; If condition (ii) is not satisfied and conditions (i) and (iii) satisfied, that is a ... See full document

... 3 Direction of Hopf bifurcation and stability of bifurcating periodic solution From Theorem 2.1 we know that model (1.2) undergoes Hopf bifurcations near E ∗ at τ = τ k j and that a family homogeneous and ... See full document

... single-species model with stage structure was studied by Aiello and Freedman ...a ratio- dependent predator-prey model with stage structure for the ... See full document

... Hopf bifurcation is how to obtain the existence of Turing–Hopf ...appropriate bifurcation parameters such that the Hopf and Turing bifurcation line in a double parameters plane can be defined by a ... See full document

... species predator-prey model is developed where prey is affected by over-harvesting and drought and predator is affected by ...on predator-prey system, and suggest ... See full document

... in predator-prey system [25]-[31], since the current birth rate of the predator is related to its consumption of prey throughout the past ...delayed predator-prey model ... See full document

... structured prey-predator model with linear functional response is proposed and ...for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary ... See full document

... Hopf bifurcation and stability of the bifurcating periodic solution of the controlled system are ...Hopf bifurcation and stable bifurca- tion periodic solutions are in excellent agreement with theoretical ... See full document

... Abstract—This paper deals with a delayed three-level food chain model with Beddington-DeAngelis functional response. By using the differential inequality theory, a set of sufficient conditions are obtained for the ... See full document

... Many differential equations cannot be solved using symbolic computation (“analysis”). For practical purposes, people sometimes construct difference equation to approximate differential equation so that they can write code ... See full document