scholarly journals Bifurcations in a predator–prey model with general logistic growth and exponential fading memory

2017 ◽  
Vol 45 ◽  
pp. 134-147 ◽  
Author(s):  
Rodrigo Castro ◽  
Willy Sierra ◽  
Eduardo Stange
Keyword(s):  
Logistic Growth ◽  
Fading Memory ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lei Hang ◽  
Long Zhang ◽  
Xiaowen Wang ◽  
Hongli Li ◽  
Zhidong Teng
Keyword(s):  
Global Attractivity ◽  
Seasonal Succession ◽  
Hybrid Population ◽  
Logistic Growth ◽  
Ultimate Boundedness ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results

AbstractIn this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz growth, and it turns to the logistic growth in the second subsystem since seasonal succession. The two processes are connected by impulsive perturbations. Some very general, weak criteria on the ultimate boundedness, permanence, existence, uniqueness and global attractivity of predator-free periodic solution are established. We find that the hybrid population model with seasonal succession has more survival possibilities of natural species than the usual population models. The theoretical results are illustrated by special examples and numerical simulations.

scholarly journals A Predator-Prey Model with Logistic Growth for Constant Delayed Migration

2020 ◽  
pp. 51-61
Author(s):  
Apima Bong'ang'a Samuel
Keyword(s):  
Human Activities ◽  
Natural Habitat ◽  
Logistic Growth ◽  
Predator Prey ◽  
Migration Rates ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models

Predator prey models predict a broad range of results depending on characteristics of predators, prey and the environment in which they interact. The environment in which these species live in and interact is usually made up of many patches, and these patches are connected via migration. The instantaneous migration of these species from one patch to another may not be realistic since there may be barriers during migration such as a busy infrastructure through the natural habitat. A predator-prey model, with logistic growth for both species and constant delayed migration, is developed and analyzed in this paper. It is shown that these species will survive if they migrate at higher rates in search of sustaining resources. Thus, for the species to coexist, we recommend that factors that slow down migration rates should be addressed, for example, reducing human activities and settlement in natural habitat.

scholarly journals Examination of Stability of the Mathematical Predator-Prey Model by Observing the Distance between Predator and Prey

2019 ◽  
Vol 8 (6S3) ◽  
pp. 65-70
Keyword(s):  
Growth Model ◽  
Equilibrium Points ◽  
Predation Rate ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Defense Behavior ◽  
Long Distance ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Maintaining distance is one of the strategies that can be applied by prey to defend themselves or to avoid predatory attacks. This defense behavior can affect predation rates. The distance or difference in the number of prey and predator populations will affect the level of balanced ecosystem. The distance is also affecting predation rate, when there’s a long distance between prey and predator thus the predation rate decreases and vice versa. The purpose of this thesis is to analyze the stability of the mathematical equilibrium on predator-prey model by observing the distance. There are two types of model being observed, type one uses exponential growth model and type two is using a logistic growth model. The analytics results obtain three equilibrium points, namely the unstable extinction equilibrium point, and the asymptotically stable predator extinction with certain conditions and asymptotically stable coexistence with certain conditions. Then numerical simulation is conducted to support the analytical results.

EFFECT OF PARASITIC INFECTION IN THE LESLIE–GOWER PREDATOR–PREY MODEL

2008 ◽  
Vol 16 (03) ◽  
pp. 425-444 ◽  
Author(s):  
MAINUL HAQUE ◽  
EZIO VENTURINO
Keyword(s):  
Biological Control ◽  
Control Parameter ◽  
Disease Incidence ◽  
Parasitic Infection ◽  
Logistic Growth ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

The Leslie–Gower predator–prey model with logistic growth in prey is here modified to include an SI parasitic infection affecting the prey population only. Thresholds are identified for the predator population to survive, and the conditions for the disease to die out naturally are given. The behavior of the system around each equilibrium is investigated, showing that the disease incidence may have a relevant influence on the dynamics of complex ecosytems, assuming at times the role of a biological control parameter.

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