Narrow Results

A biologically feasible continuous time model of a three level food web consisting of a specialist and a generalist predator is investigated. The boundedness of the unique solution of the model establishes the dissipative nature of the food web. Necessary and sufficient criteria for the coexistence of the three interacting populations are established. Complex behavior of the system is evident from the bifurcation diagrams. Abundance of periodic and chaotic behavior of the species with the variation of the key parameters are also observed. The strange attractors for the time evolution of the coexisting species are drawn.

Non-autonomous dynamical systems generate cocycles w.r.t. a flow. We give conditions for the existence of attractors for cocycles based on the so-called pull back convergence. These conditions will be applied to the non-autonomous Navier Stokes equation. In particular. we do not need compactness assumption for the time dependent coefficients of this equation.