Equilibrium, stability and chaotic behavior in Leslie matrix models with different density-dependent birth and survival rates

Nonlinear modified Leslie matrix models with different density-dependent birth and survival rates are analyzed. Conditions for the existence and uniqueness of a positive equilibrium state are discussed. In the case of exponential density dependence the conditions for local stability of a three-dimensional model are derived. An invariant equilibrium surface, containing all equilibrium points of this model, is constructed. Special cases which the age structure remains unchanged in spite of density effects on the vital rates are considered. The existence of chaotic behavior is demonstrated. The nonlinear systems of difference equations were analyzed and solved using MAPLE.