The main objective of the present paper is to consider the dynamical analysis of a three dimensional prey-predator model within deterministic environment and the influence of environmental driving forces on the dynamics of the model system. For the deterministic model we have obtained the local asymptotic stability criteria of various equilibrium points and derived the condition for the existence of small amplitude periodic solution bifurcating from interior equilibrium point through Hopf bifurcation. We have obtained the parametric domain within which the model system exhibit chaotic oscillation and determined the route to chaos. Finally, we have shown that chaotic oscillation disappears in presence of environmental driving forces which actually affect the deterministic growth rates. These driving forces are unable to drive the system from a regime of deterministic chaos towards a stochastically stable situation. The stochastic stability results are discussed in terms of the stability of first and second order moments. Exhaustive numerical simulations are carried out to validate the analytical findings.
Upadhyay, R. K., Banerjee, M., Parshad, R., & Raw, S. N. (2011). Deterministic chaos versus stochastic oscillation in a prey-predator-top predator model. Mathematical Modelling and Analysis, 16(3), 343-364. https://doi.org/10.3846/13926292.2011.601767
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
