Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population

2020 ◽  
Vol 138 ◽  
pp. 109960 ◽  
Author(s):  
Behzad Ghanbari ◽  
Salih Djilali
Keyword(s):  
Social Behavior ◽  
Fractional Order ◽  
Mathematical Analysis ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

scholarly journals Analysis for fractional‐order predator–prey model with uncertainty

2019 ◽  
Vol 13 (6) ◽  
pp. 277-289 ◽  
Author(s):  
Samayan Narayanamoorthy ◽  
Dumitru Baleanu ◽  
Kalidas Thangapandi ◽  
Shyam Sanjeewa Nishantha Perera
Keyword(s):  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

A fractional-order predator–prey model with Beddington–DeAngelis functional response and time-delay

2018 ◽  
Vol 27 (2) ◽  
pp. 525-538 ◽  
Author(s):  
Rajivganthi Chinnathambi ◽  
Fathalla A. Rihan ◽  
Hebatallah J. Alsakaji
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals A new study for the global asymptotic stability of a general predator-prey model

2021 ◽  
Author(s):  
Manh Tuan Hoang
Keyword(s):  
Asymptotic Stability ◽  
Functional Response ◽  
Mathematical Analysis ◽  
Global Asymptotic Stability ◽  
Lyapunov Stability Theory ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Theoretical Results

In a previous paper [L. M. Ladino, E. I. Sabogal, Jose C. Valverde, General functional response and recruitment in a predator-prey system with capture on both species, Math. Methods Appl. Sci. 38(2015) 2876-2887], a mathematical model for a predator-prey model with general functional response and recruitment including capture on both species was formulated and analyzed. However, the global asymptotic stability (GAS) of this model was only partially resolved. In the present paper, we provide a rigorously mathematical analysis for the complete GAS of the predator-prey model. By using the Lyapunov stability theory in combination with some nonstandard techniques of mathematical analysis for dynamical systems, the GAS of equilibria of the model is determined fully. The obtained results not only provide an important improvement for the population dynamics of the predator-prey model but also can be extended to study its modified versions in the context of fractional-order derivatives. The theoretical results are supported and illustrated by a set of numerical examples.

scholarly journals Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey

2019 ◽  
Vol 2 (2) ◽  
pp. 105 ◽  
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumahwinahyu ◽  
Isnani Darti
Keyword(s):  
Infectious Diseases ◽  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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