A Beddington–DeAngelis type one-predator two-prey competitive system with help

A Beddington–DeAngelis type one-predator two-prey competitive system with help Nonlinear Dyn https://doi.org/10.1007/s11071-018-4377-9 ORIGINAL PAPER A Beddington–DeAngelis type one-predator two-prey competitive system with help Jai Prakash Tripathi · Debaldev Jana · Vandana Tiwari Received: 17 April 2017 / Accepted: 24 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, we present and study a two manence of the system and examine the role of coop- competing prey and one predator system where during eration coefficient. Different conditions for the coexis- predation both the teams of prey help each other and the tence of equilibrium solutions are discussed. Then the rate of predation on both the teams are different. The local asymptotic stability of various equilibrium points prey consumption rate per individual of predator is con- and the existence of Hopf bifurcation at the positive sidered as Beddington–DeAngelis type. Beddington– equilibrium are carried out to understand the dynam- DeAngelis type functional response describes predator ics of the model system. The Kolmogorov analysis of feeding rate depending on both the prey and preda- subsystems suggests for the existence of transcritical tor density. Ecological significance of considering this bifurcation. Sufficient conditions for the nonexistence type of functional response depends on how frequently of periodic orbits http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

A Beddington–DeAngelis type one-predator two-prey competitive system with help

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-018-4377-9
Publisher site
See Article on Publisher Site

Abstract

Nonlinear Dyn https://doi.org/10.1007/s11071-018-4377-9 ORIGINAL PAPER A Beddington–DeAngelis type one-predator two-prey competitive system with help Jai Prakash Tripathi · Debaldev Jana · Vandana Tiwari Received: 17 April 2017 / Accepted: 24 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, we present and study a two manence of the system and examine the role of coop- competing prey and one predator system where during eration coefficient. Different conditions for the coexis- predation both the teams of prey help each other and the tence of equilibrium solutions are discussed. Then the rate of predation on both the teams are different. The local asymptotic stability of various equilibrium points prey consumption rate per individual of predator is con- and the existence of Hopf bifurcation at the positive sidered as Beddington–DeAngelis type. Beddington– equilibrium are carried out to understand the dynam- DeAngelis type functional response describes predator ics of the model system. The Kolmogorov analysis of feeding rate depending on both the prey and preda- subsystems suggests for the existence of transcritical tor density. Ecological significance of considering this bifurcation. Sufficient conditions for the nonexistence type of functional response depends on how frequently of periodic orbits

Journal

Nonlinear DynamicsSpringer Journals

Published: Jun 4, 2018

References

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