Chaotic dynamics of a three species prey-predator competition model with noise in ecology

Applied Mathematics and Computation

Volumn 231, Issue , 2014, Pages 117-133

  Das, Kalyan ^a   Shiva Reddy, K ^b   Srinivas, M N ^c   Gazi, N H ^d  

^a NATIONAL INSTITUTE OF FOOD TECHNOLOGY ENTREPRENEURSHIP AND MANAGEMENT   (India)

^b ANURAG UNIVERSITY   (India)

^c VIT UNIVERSITY   (India)

^d Aliah University   (India)

Author keywords

Chaos; Fourier transform methods; Local and global stability; Lyapunov function; Prey predator; Routh Hurwitz criteria; Stochastic delayed perturbation; Top predator

Indexed keywords

DELAYED PERTURBATION; FOURIER TRANSFORM METHOD; LOCAL AND GLOBAL STABILITIES; PREY-PREDATOR; ROUTH-HURWITZ; TOP PREDATOR;

CHAOS THEORY; COMPUTER SIMULATION; ECOLOGY; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS;

STABILITY CRITERIA;

EID: 84893106602     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.12.182     Document Type: Article

References (21)

1. V. Volterra Leçons sur la théorie mathématique de la lutte pour la vie 1931 Gauthier-Villars Paris
2. A.J. Lokta Elements of Physical Biology 1925 Williams and Wilkins Baltimore
3. W.J. Meyer Concepts of Mathematical Modelling 1985 McGraw-Hill
4. J.M. Cushing Integro-differential Equations and Delay Models in Population Dynamics Lecture Notes in Biomathematics vol. 20 1997 Springer-Verlag Heidelberg
5. Paul Colinvaux Ecology 1986 John Wiley and Sons Inc. New York
6. H.I. Freedman Deterministic Mathematical Models in Population. Ecology 1980 Marces-Decker New York
7. George F. Simmons Differential Equations with Applications and Historical Notes 1974 Tata McGraw-Hill New Delhi
8. J.N. Kapur, Mathematical Models in Biology and Medicine Affiliated East-West, 1985.
9. N.C. Srinivas, Some Mathematical Aspects of Modeling in Bio Medical Sciences (Ph.D. thesis), Kakatiya University, 1991.
10. K. Lakshmi Narayan, A Mathematical Study of Prey-Predator Ecological Models with a Partial Covers for the Prey and Alternative Food for the Predator (Ph.D. thesis), J.N.T. University, 2004.
11. C.S. Holling Resilience and stability of ecological systems Ann. Rev. Ecol. Syst. 4 1973 1 23
12. J. Ripa, and P. Lundberg Noise colour and the risk of population extinction Proc. R. Soc. Lond. B 263 1996 1751 1753
13. C. Xu, and Z. Li Population dynamics and the color of environmental noise: a study on a three-species food chain system Ecol. Res. 18 2003 145 154 (Pubitemid 36391804)
14. G.Q. Sun, Z. Jin, L. Li, and Q.X. Liu The role of noise in a predator-prey model with Allee effect J. Biol. Phys. 35 2009 185 196
15. Wenting Wang, Wenlong Li, Zizhen Li, and Hui Zhang The effect of colored noise on spatiotemporal dynamics of biological invasion in a diffusive predator-prey system Bio Syst. 104 2011 48 56
16. Margherita Carletti Numerical simulation of a Campbell-like stochastic delay model for bacteriophage infection Math. Med. Biol. (an IMA Journal) 23 2006 297 310 (Pubitemid 44896816)
17. B. Ravindra Reddy, K. Lakshmi Narayan, and N.Ch. Pattabhiramacharyulu A model of two mutually interacting species with limited resources for both the species Int. J. Eng. Res. Indus. Appl. 2 II 2009 281 291
18. T.K. Kar, and M. Swarnakamal Influence of prey reserve in a prey-predator fishery Non-Linear Anal. 65 2006 1725 1735
19. K. Shiva Reddy, K. Lakshmi Narayan, and N.Ch. Pattabhiramacharyulu A three species ecosystem consisting of a prey, predator and super predator Math. Appl. Sci. Technol. 2 1 2010 95 107
20. R.M. Nisbet, and W.S.C. Gurney Modelling Fluctuating Populations 1982 John Wiley New York
21. M. Carletti Numerical solution of stochastic differential problems in the biosciences J. Comput. Appl. Math. 185 2006 422 440 (Pubitemid 41354348)