| Citation: |
Qianjun Chen, Zijian Liu, Yuanshun Tan, Jin Yang. ANALYSIS OF A STOCHASTIC NONAUTONOMOUS HYBRID POPULATION MODEL WITH IMPULSIVE PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2365-2386. doi: 10.11948/20220108
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ANALYSIS OF A STOCHASTIC NONAUTONOMOUS HYBRID POPULATION MODEL WITH IMPULSIVE PERTURBATIONS
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Abstract
In this paper, we propose a stochastic nonautonomous hybrid population model with Allee effect, Markovian switching and impulsive perturbations and investigate its stochastic dynamics. We first establish sufficient conditions for the extinction and permanence. Then, we study some asymptotic properties and the lower- and upper-growth rates of the positive solutions. Finally, by performing numerical simulations we verify the main results and analyze the impact on the system from the Allee effect, the Markovian switching and the impulsive perturbations.
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Keywords:
- Allee effect /
- markovian switching /
- impulsive perturbations /
- permanence /
- extinction
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References
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Qianjun Chen, Zijian Liu, Yuanshun Tan, Jin Yang. ANALYSIS OF A STOCHASTIC NONAUTONOMOUS HYBRID POPULATION MODEL WITH IMPULSIVE PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2365-2386. doi: 10.11948/20220108
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Figure 1.
Figure (a) represents the trajectory of the solution of subsystem (5.1a). It is shown that population
$ x $ -
Figure 2.
Trajectories of system (5.1) switching between states 1 and 2. Figure (a) represents the trajectory of the stationary distribution
$ \pi=(\pi_1, \pi_2)=(0.7, 0.3) $ $ x $ $ \pi=(\pi_1, \pi_2)=(0.2, 0.8) $ -
Figure 3.
Trajectories of system (5.1) switching between states 1 and 2, the stationary distribution of Markov chain is
$ \pi=(\pi_1, \pi_2)=(0.7, 0.3) $ $ (\sigma(t, 1), \sigma(t, 2))=(0.5-0.1\cos t, 0.4+0.1\cos t) $ $ (\sigma(t, 1), \sigma(t, 2))=(0.8-0.1\cos t, 0.8+0.1\cos t) $ -
Figure 4.
Trajectories of system (5.1). Figure (a) represents the trajectory of the solution of subsystem (5.1a). It shows that population
$ x $ $ \pi=(\pi_1, \pi_2)=(0.7, 0.3) $ -
Figure 5.
Figure (a) represents the trajectory of the solution of subsystem (5.1a) with
$ g_k(1)=1.05 $ $ x $ $ g_k(2)=0.8 $ -
Figure 6.
Figures represent the trajectory of the solution of subsystem (5.1a).