THE EFFECT OF CORRELATION FUNCTIONS ON A NONLINEAR INTERACTION BETWEEN MULTISPECIES

Authors

  • Suzan. A. A. Abu-harbid Mathematics Department. Science Faculty. Omar Al-Mukhtar University. Al-guba-Libya
  • Abdulrahman. A. El-samman Mathematics Department. Science Faculty. Al-Azhar University. Cairo-Egypt
  • Abdelsalam. B. H. Aldaikh Mathematics Department. Science Faculty. Omar Al-Mukhtar University. El-Beida-Libya

DOI:

https://doi.org/10.53555/eijas.v1i4.22

Keywords:

Nonlinear (DES), Interacting biological system, Multispecies population, Analytic approximate solutions, Auto, cross correlation functions

Abstract

This study provides the effect of correlation functions on the solution of nonlinear differential equations system (DES). For illustration, an application of the case of interacting biological system is introduced for multispecies population, Moreover, the concept of stability and identification of equilibrium points are studied, this obtain the analytic approximate solutions. In order to evaluate the solution of the correlation functions, this study has been limited on the chronological correlation functions of the two type’s; auto and cross. That is to reach the expense of second and third- correlation functions. 

References

. Lotka AJ: Elements of Physical Biology, New York, Williams and Wilkins, 1925.

. Volterra V: Variazioni e fluttuazioni Del numerod, individui in specie animaliiiconviventi, Mem AcadLincei 3, 31-113, 1926.

. Murray JD: Mathematical biology, 2nd ed. New York, Springer, 1993.

. J. N. Kaput: Mathematical Models in Biology and Medicine, Affiliated East- WestiPress Private Limited New Delhi, 1992.

. J. N. Kapur: Stability Analysis of Continuous and Discrete Population Models, IndianiiJ. Pure Appl. Math. , Vol 9 pp 702-08, 1976.

. J. N. Kapur: Moments for Some General Birth and Death Processes, Jour. Ind. iiAcad.iMaths, Vol 1 pp 10-17,1979.

. J. N. Kapur, Umakumar: Generalised Birth and Death Processes with Twin iiiBirths,iNat Acad. Sci. Letters, Vol 1 pp 30-32,1978.

. J. N. Kapur: Predator-Prey Models with Discrete Time Lags, Nat. Acad. Sci.iLetters,iVol 2 pp 237-75,1979.

. J. N. Kapur: Application of Generalized Hypergeometric Functions to GeneralizediBirth and Death Processes, Indian J. Pure Appl. Math. Vol 9 pp i1159- 69, 1978.

. J. N. Kapur ,Q.J.A.kahan: Some Mathematical Models for Population Growth Indian J. PureAppl . Math., Vol 10 pp 277- 86, 1979.

. J. N. Kapur, F. N. A: Population Dynamics via Games Theory and Modified Volterra Equations, Indian J. Pure Appl. Math, Vol 11 pp 347-53, 1980.

. J. N. Kapur, F. N. A: Nonlinear Continuous-Time Discrete-Age-Scale PopulationiModels, Indian J. Pure Appl. Math. Vol 11 pp 682-92, 1980.

. J. N. Kapur: The Effect of Harvesting on Competing Populations, MathematicaliBiosciences, Mathematical Biosciences, Vol 51 pp 175– 85,1980.

. VlastimilkŘivan: Optimal Foraging and Predator-Prey Dynamics, Theoretical Population Biology 49,265-290,1996

. Meng For, kewang: Periodicity in a Delayed Ratio-Detention Predator- Prey iiiSystem, Journal of Mathematical Analysis and Applications 262, 179-190,2001.

. Lin QIU, Taketomo Mitsui: Predator-Prey Dynamics with Delay when Prey iiiDispersing in n-Patch Environment, Graduate School of Human Informatics, iiiNagoya University, Japan, pp 1-14,2002.

. Chris Flake, Tram Hoang, Elizabeth Perrigo: A Predator-Prey Model with iDiseaseiDynamics, Under the Direction of Dr. Glenn Ledder, Department of Mathematicsiand Statistics, University of Nebraska- Lincoln, pp 116,2003.Paul Waltman, James Braselton, and Lorraine Braselton: A Mathematical Model ofia Biological Arms Race with a Dangerous Prey, J. Theor Biol, 218, 55-i70,2002.

. Ross Cressman, J. Garey: Evolutionary Stability in Lotka-Volterra Systems, J ofiiTheoretical Biology, 222, 233-245, 2003.

. Yan Ni Xiao, Lan sun Chen: Global Stability of a Predator-Prey System with Stagei Structure for the Predator, Acta Mathematica Sinica, English Series, Vol. ii19, No .i2, pp. 1-11, 2003.

. PATRICK C. TOBIN, OTTAR N. BJØRNSTAD: Spatial Dynamics and Cross-iCorrelation in a Transient Predator-Prey System, Journal of Animal Ecology, 72, -467, 2003.

. Volkan Sevim, Per Arne Rikvold: Effects of Correlated Interactions in a BiologicaliCoevolution Model with Individual-Based Dynamics, J. Phys. A. ii math .Gen. 38, -9489, 2005.

. A. F. Rozenfeld, C. J, Tessone, E. Albano and H. S .wio: On the InfluesnceiiofiiNoise on the Critical and Oscillatory Behavior of a Predator-Prey Model:iiCoherentiStochastic Resonance at the Proper Frequency of the System, aleroz @ iinifta. unlp.iedu. ar, pp 1-18, (March 2006).

. B. Batiha, M. S. M. Noorani, I. Hashim: Variational Iteration Method for Solving iiiiMultispecies Lotka-Volterra Equations, Computers and Mathematics with iApplications 24, 903-909, 2007.

. Jing Ruan, Yanhua Tan, Changsheng Zhang: A Modified Algorithm for iiiiApproximate Solutions of Lotka-Volterra Systems, Procedia Engineering 15, iiii1493-1497, 2011.

. Nicola Serra: Utility Functions and Lotka-Volterra Model: A Possible Connection iiiniiPredator-Prey Game, Journal of Game Theory, 3(2), 31-34, 2014.

. Susmita Paul, Sankar Prasad Mondal, Paritosh Bhattacharya: Numerical Solution iiofiiLotka-Voiterra Prey Predator Model by Using Runge-Kutta-Fehlberg Method iiiandiiLaplace Adomian Decomposition Method, Alexandria Engineering Journal iiii55, 613-i617, 2016.

. YiğitAksoy, ÜnalGöktaş, Mehmet Pakdemirli, IhsanTimuçinDolapçı: Application iiof Perturbation-Iteration Method to Lotka-Volterra Equations, iiAlexandria Engineering Journali55, 1661-1666, 2016.

. Noura A. Abdulrazaq Tahar, Analysis of Hybrid Dynamical Systems with aniiApplication in Biological Systems, Thesis of Master, Çankaya University,2017.

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Published

2015-12-27