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Deterministic Stabilization of a Dynamical System using a Computational Approach
( Vol-4,Issue-1,January 2018 )


Isobeye George, Jeremiah U. Atsu, Enu-Obari N. Ekaka-a


Deterministic, stabilization, dynamical system, steady-state solution, changing initial data.


The qualitative behavior of a multi-parameter dynamical system has been investigated. It is shown that changes in the initial data of a dynamical system will affect the stabilization of the steady-state solution which is originally unstable. It is further shown that the stabilization of a five-dimensional dynamical system can be used as an alternative method of verifying qualitatively the concept of the stability of a unique positive steady-state solution. These novel contributions have not been seen elsewhere; these are presented and discussed in this paper.

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Agarwal, M. and Devi, S. (2011). A resource-dependent competition model: Effects of toxicant emitted from external sources as well as formed by precursors of competing species. Nonlinear Analysis: Real World Application, 12, 751-766.
Akpodee, R. E. and Ekaka-a, E. N. (2015). Deterministic stability analysis using a numerical simulation approach, Book of Proceedings – Academic Conference Publications and Research International on Sub-Sahara African Potentials in the new Millennium, 3(1).
Chattopadhyay, J. (1996). Effects of toxic substances on a two-species competitive system, Ecological Model, 84, 287 – 289.
Dhar, J., Chaudhary, M. and Sahu, G. P. (2013). Mathematical model of depletion of forestry resource, effect of synthetic-based industries. International Journal of Biological, Life Science and Engineering, 7, 1 – 5.
De Luna, J. T. and Hallam, T. G. (1987). Effects of toxicants on populations: a qualitative approach IV. Resource-consumer-toxicant model, Ecological Model, 35, 249 – 273.
Dubey, B. and Hussain, J. (2000). A model for allelopathic effect on two competing species, Ecological Model, 129, 195 – 207.
Ekaka-a, E. N. (2009). Computational and mathematical modeling of plant species interactions in a harsh climate, Ph. D Thesis, University of Liverpool and University of Chester, United Kingdom.
Freedman, H. I. and Shukla, J. B. (1991). Models for the effect of toxicant in singlespecies and predator-prey systems, Journal of Mathematical Biology, 30, 15-30.
Freedman, H. I. and So, J. W. H. (1985). Global stability and persistence of simple food chains, Mathematical Bioscience, 76,69-86.
Garcia-Montiel, D. C. and Scantena, F. N. (1994). The effects of human activity on the structure composition of a tropical forest in Puerto Rico, Forest Ecological Management, 63, 57 – 58.
Hallam, T. G., Clark, C. E., and Jordan, G. S. (1983). Effects of toxicants on populations: a qualitative approach II. First order kinetics, Journal of Mathematical Biology, 18, 25 – 37.
Hallam, T. G., Clark, C. E., and Lassiter, R. R. (1983). Effects of toxicants on populations: a qualitative approach I. Equilibrium environmental exposure. Ecological Model, 18, 291-304.
Hallam T. G. and De Luna, J. T. (1984). Effects of toxicants on populations: a qualitative approach III. Environmental and food chain pathways, Journal of Theoretical Biology, 109, 411 – 429.
Hsu, S. B., Li, Y. S. and Waltman, P. (2000). Competition in the presence of a lethal external inhibitor, Mathematical Bioscience,, 167, 177 – 199.
Hsu, S. B. and Waltman, P (1998). Competition in the chemostat when one competitor produces a toxin, Japan Journal of Industrial and Applied Mathematics, 15,471–490.
Huaping, L, and Zhien, M. (1991). The threshold of survival for system of two species in a polluted environment, Journal of Mathematical Biology, 30, 49 – 61.
Lancaster, P. L. and Tismenetsky, M (1985).The Theory of Matrices, Second Edition, Academic Press, New York.
Rescigno, A. (1977). The struggle for life – V. One species living in a limited environment, Bulleting of Mathematical Biology, 39, 479 – 485.
Shukla, J. B., Agarwal, A., Dubey, B. and Sinha, P. (2001). Existence and survival of two competing species in a polluted environment: a mathematical model, Journal of Biological Systems, 9(2), 89 – 103.
Shukla, J. B., Sharma, S., Dubey, B. and Sinha, P. (2009). Modeling the survival of a resource-dependent population: Effects of toxicants (pollutants) emitted from external sources as well as formed by its precursors, Nonlinear Analysis: Real World Application, 54-70.
Thieme, H. R. (2000). Uniform persistence and permanence for non-autonomous semi-flows in population biology, Mathematical Bioscience, 166,173-201.
Yan, Y. and Ekaka-a, E. N. (2011). Stabilizing a mathematical model of population system, Journal of the Franklin Institute, 348(10), 2744 – 2758.
Zhien, M. and Hallam, T. G. (1987). Effects of parameter fluctuations on community survival. Mathematical Bioscience, 86,35 – 49.