Advances in Differential Equations and Control Processes
Volume 10, Issue 2, Pages 89 - 111
(November 2012)
|
|
STOCHASTIC CHAOS IN A CLASS OF FOKKER-PLANCK EQUATIONS DERIVED FROM POPULATION DYNAMICS
S. Moussiliou, S. Massou, S. Mounmouni and M. Tchoffo
|
Abstract: In this work, we obtain results by using a physical potential whose parameters have biological significance [5] to explain the interaction between two species in population dynamics. In using the degenerated parameters [8], this potential is reduced to the form of where m is the coupling constant. Consequently, we study the effect of this constant on the potential The deterministic chaos results are obtained in Figures 2 and 3. An interesting result of our theoretical model resides in the fact that after many manifestations of the deterministic chaos, the physical potential remained unchanged above a critical value This situation corresponds without any doubt to the Hopf bifurcation in the nonlinear system, where the stationary effect changes to the unstable to stable and leads to a limit cycle. Then we studied the manifestations of the stochastic chaos by considering the transformed potential where is the noise intensity. In such a case the combined effect of the noise and the coupling constant, gives results as illustrated in Figures 4 and 5. The second model [5] leads to a potential with two coupling constants which indicate that the use of degenerated parameter is strictly forbidden. The results obtained show the chaotic behavior of the potential for the arbitraries values of coupling constants Figures 6 and 7. The stochastic manifestations are also shown by the transformed potential Figures 8 and 9. |
Keywords and phrases: |
|
Number of Downloads: 263 | Number of Views: 780 |
|