Stochastic modeling of plant-insect interaction dynamics with MEMS-based monitoring and noise effects

Abstract

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The dynamics of plant-insect interactions play a crucial role in the ecosystem, influenced by complex molecular signaling pathways. This study extends existing deterministic models of plant-insect systems by incorporating stochastic elements and molecular interactions, particularly focusing on the roles of Botrytis Induced Kinase-1 (BIK1) and Phyto Alexin Deficient-4 (PAD4) proteins. The model evaluates the effects of constant inhibition, pulsed inhibition, and adaptive feedback control on plant biomass (y1), insect herbivore density (y2), PAD4 levels (y3), and BIK1 levels (y4). Additionally, we examine the impact of different noise types, including deterministic, Gaussian, and Lévy noise, on system variability and stability. Results indicate that our stochastic model is superior as it shows a significant reduction in BIK1 levels, particularly under higher noise intensities, which enhances PAD4 activity and improves plant defense mechanisms. Moreover, moderate noise intensity (σ=0.05) provides an optimal balance, sustaining PAD4 levels while effectively controlling insect herbivore populations. We also integrate MEMS-based feedback mechanisms, which dynamically adjust plant biomass and molecular signaling, further stabilizing the system’s response to environmental variability.

Keywords

• mathematical analysis
• feedback mechanism
• immunity dynamics
• Lévy noise
• MEMS