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Hari Prasad, B.
- A Study on Discrete Model of a Prey-Predator Ecosystem with Limited and Unlimited Resources
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Authors
Affiliations
1 Department of Mathematics, Chaitanya Degree College (Autonomous) Hanamkonda, 506 001, IN
1 Department of Mathematics, Chaitanya Degree College (Autonomous) Hanamkonda, 506 001, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 169-179Abstract
In this paper, we study on discrete model of two interacting species a prey-predator eco-system with limited and unlimited resources. The system comprises of a prey (S1), a predator (S2) that survives upon S1. The basic equations for this model constitute as two first order non-linear coupled ordinary difference equations. All possible equilibrium points are identified based on the model equations and criteria for their stability are discussed. The model would be stable if absolute value of each of the eigen values of the characteristic equation is less than one.Keywords
Eigen Value, Equilibrium Point, Prey, Predator, Stable.
- Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources
Abstract Views :253 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Chaitanya Group of Colleges (Autonomous), Hanamkonda, IN
1 Department of Mathematics, Chaitanya Group of Colleges (Autonomous), Hanamkonda, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 126-136Abstract
The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S1, S2 and one commensal species S3. Further, S1 and S2 are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic ischolar_mains are negative, in case they are real, and have negative real parts, in case they are complex. Trajectories of the perturbations over the equilibrium states are illustrated. Further the global stability of the system is established with the aid of suitably constructed Liapunov's function.Keywords
Commensal, Equilibrium State, Host, Neutral, Stable, Trajectories, Unstable.References
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