| Citation: |
Tiansi Zhang, Lihong Qiu, Dianli Zhao, Sanling Yuan. OSCILLATION AND SURVIVAL ANALYSIS OF GENERALIZED STOCHASTIC LOGISTIC MODELS WITH PIECEWISE CONSTANT ARGUMENT[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1522-1542. doi: 10.11948/20230271
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OSCILLATION AND SURVIVAL ANALYSIS OF GENERALIZED STOCHASTIC LOGISTIC MODELS WITH PIECEWISE CONSTANT ARGUMENT
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Abstract
The paper focuses on oscillation and survival analysis for a class of generalized stochastic logistic equations with piecewise constant argument. The existence of global positive solution is proved firstly. Then the necessary and sufficient conditions under which the population will be almost surely extinct and persistent are investigated. Furthermore, we study the condition for oscillation of the equation with constant coefficients, and the result shows that the solution oscillates around a new positive point induced by the noise. Finally, numerical experiments are given for several examples to support the results.
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References
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Tiansi Zhang, Lihong Qiu, Dianli Zhao, Sanling Yuan. OSCILLATION AND SURVIVAL ANALYSIS OF GENERALIZED STOCHASTIC LOGISTIC MODELS WITH PIECEWISE CONSTANT ARGUMENT[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1522-1542. doi: 10.11948/20230271
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Figure 1.
(a) : the trajectory of the determined equation (5.3). (b) : the trajectory of the stochastic equation (5.2) with
$ \Delta t=0.001 $ -
Figure 2.
(c): the trajectory of equation (5.4) with
$ \Delta t=0.001 $ $ X(t) $ -
Figure 3.
The blue line in (e) is the trajectory of equation (5.5) with
$ \Delta t=0.001 $ $ X(t) $ $ \widetilde{x}= 0.655 $