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

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 ( y 1 ) , insect herbivore density ( y 2 ) , PAD4 levels ( y 3 ) , and BIK1 levels ( y 4 ) . Additionally, we examine the impact of different noise types, including deterministic, Gaussian, and L & eacute;vy 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 ( sigma = 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.