| Citation: |
Tangjiarui Chen, Yue Meng, Zhigui Lin. PERSISTENCE AND EXTINCTION OF A PEST-NATURAL ENEMY DIFFUSIVE MODEL WITH BIRTH AND HARVESTING IMPULSES[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 453-472. doi: 10.11948/20260076
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PERSISTENCE AND EXTINCTION OF A PEST-NATURAL ENEMY DIFFUSIVE MODEL WITH BIRTH AND HARVESTING IMPULSES
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Abstract
To understand how birth pulses and human interventions jointly influence the spatial dynamics of pests and their natural enemies, this paper develops an impulsive reaction-diffusion model for a pest-natural enemy system. We first investigate the principal eigenvalue of a corresponding single-species eigenvalue problem using the Krein-Rutman theorem and establish its monotonicity with respect to impulse intensities. Based on these eigenvalues, we analyze the threshold dynamical behavior of the full model. Sufficient conditions for co-extinction, single-species persistence, and two-species coexistence are derived. Compared with existing impulsive models that focus on either single species or single impulsive event, our work explicitly couples birth pulses and harvesting impulses in a two-species reaction-diffusion framework. The eigenvalue-based threshold criteria extend the classical logistic impulsive theory to predator-prey interactions with spatial heterogeneity. Finally, numerical simulations are presented to illustrate the theoretical results and to explore the impact of birth pulses and human interventions on population dynamics.
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Keywords:
- Diffusive model /
- pulse /
- threshold value /
- persistence /
- extinction
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References
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Tangjiarui Chen, Yue Meng, Zhigui Lin. PERSISTENCE AND EXTINCTION OF A PEST-NATURAL ENEMY DIFFUSIVE MODEL WITH BIRTH AND HARVESTING IMPULSES[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 453-472. doi: 10.11948/20260076
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Figure 1.
Simulation for
$ \beta=0.3 $ $ \gamma=0.6 $ $ \mu_u\approx0.047>0 $ $ \mu_v\approx0.047>0 $ $ x=\pi/2 $ -
Figure 2.
Simulations for
$ \beta=0.3 $ $ \gamma=0.9 $ $ \mu_u \approx0.047>0, \mu_v \approx-0.125<0 $ $ (a)-(f) $ -
Figure 3.
Simulations for
$ \beta=0.15 $ $ \gamma=0.6 $ $ \mu_u^* < 0, \mu_v^* < 0 $ $ \mu_{v}^{**} < 0 $ $ (a)-(f) $