TY - JOUR
T1 - Persistence and global stability of bazykin predator-prey model with beddington-deangelis response function
AU - Sarwardi, Sahabuddin
AU - Haque, Mainul
AU - Mandal, Prashanta Kumar
N1 - Funding Information:
The authors Mr. S. Sarwardi and Dr. P. K. Mandal gratefully acknowledge the financial support in part from Special Assistance Programme (SAP-II) sponsored by University Grants Commission (UGC) , New Delhi, India.
PY - 2014/1
Y1 - 2014/1
N2 - In this article, a predator-prey model of Beddington-DeAngelis type with discrete delay is proposed and analyzed. The essential mathematical features of the proposed model are investigated in terms of local, global analysis and bifurcation theory. By analyzing the associated characteristic equation, it is found that the Hopf bifurcation occurs when the delay parameter τ crosses some critical values. In this article, the classical Bazykin's model is modified with Beddington-DeAngelis functional response. The parametric space under which the system enters into Hopf bifurcation for both delay and non-delay cases are investigated. Global stability results are obtained by constructing suitable Lyapunov functions for both the cases. We also derive the explicit formulae for determining the stability, direction and other properties of bifurcating periodic solutions by using normal form and central manifold theory. Our analytical findings are supported by numerical simulations. Biological implication of the analytical findings are discussed in the conclusion section.
AB - In this article, a predator-prey model of Beddington-DeAngelis type with discrete delay is proposed and analyzed. The essential mathematical features of the proposed model are investigated in terms of local, global analysis and bifurcation theory. By analyzing the associated characteristic equation, it is found that the Hopf bifurcation occurs when the delay parameter τ crosses some critical values. In this article, the classical Bazykin's model is modified with Beddington-DeAngelis functional response. The parametric space under which the system enters into Hopf bifurcation for both delay and non-delay cases are investigated. Global stability results are obtained by constructing suitable Lyapunov functions for both the cases. We also derive the explicit formulae for determining the stability, direction and other properties of bifurcating periodic solutions by using normal form and central manifold theory. Our analytical findings are supported by numerical simulations. Biological implication of the analytical findings are discussed in the conclusion section.
KW - Delay
KW - Ecological models
KW - Global stability
KW - Hopf bifurcation
KW - Local stability
KW - Numerical simulation
KW - Permanence
KW - Population models
UR - http://www.scopus.com/inward/record.url?scp=84884143415&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2013.05.029
DO - 10.1016/j.cnsns.2013.05.029
M3 - Article
AN - SCOPUS:84884143415
SN - 1007-5704
VL - 19
SP - 189
EP - 209
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 1
ER -