Basin Transition and Alternative States: Role of Multi-species Herbivores-Induced Volatile in Plant-Insect Interactions.

A simple model on volatile organic compound (VOC)-mediated plant-insect interactions is proposed and examined here, when two different classes of herbivorous insects competing for a common resource (plant) in the presence of a specialist carnivorous enemy, which only predates one of the herbivore species. We, particularly, emphasize the impact of VOCs on plant's growth fitness. The system experiences several local and global bifurcations with emergent alternative states for variations in recruitment factors and predation rate. Basin transitions and basin of attractions have provided detail descriptions on the selectivity of the alternative states, when only one of the herbivore species can survive depending on the choice of initial population densities of the interacting species and how it provides a steady growth in plant. Additionally, our results support the concept of competitive exclusion principle in an indirect interspecific competition between the two herbivore types for the common resource, plant.

Deterministic and stochastic analysis of an eco-epidemiological model.

Chronic wasting disease (CWD) is a contagious prion disease among the deer family that has the potential to disrupt the ecosystems where deer occur in abundance. To understand the dynamics of this emerging infectious disease, we consider a simple eco-epidemic model where the host population is infected by CWD. Boundedness of the system is established. The structure of equilibria and their linearized stability are investigated. The persistence condition is discussed. By constructing a suitable Lyapunov function, we discuss the global stability of the endemic equilibrium. Local bifurcation (transcritical) around the boundary equilibria is developed. Sufficient conditions for the existence of Hopf-bifurcation are derived. Further, we have also introduced white type of noise into the system to investigate stochastic stability. This suggests that the deterministic model is robust with respect to stochastic perturbation. Some numerical simulations are performed to validate our results.

A delayed prey-predator system with parasitic infection.

This paper analyzes a prey-predator system in which some members of the prey population and all predators are subjected to infection by a parasite. The predator functional response is a function of a weighted sum of prey abundances. Persistence and extinction criteria are derived. The stability of the interior equilibrium point is discussed. The role of delay is also addressed. Lastly the results are verified through computer simulation. Numerical simulation suggests that the delay has a destabilizing effect.