A finite difference approximation to a hierarchical size-structured model with nonlinear
growth, mortality and reproduction rates is developed. Existence-uniqueness of the weak …

We present a survey of new approaches to the investigation of the global dynamics of
discrete dynamical systems or autonomous difference equations. To achieve our objectives …

We present a hierarchically size-structured population model with growth, mortality and
reproduction rates which depend on a function of the population density (environment). We …

ABSTRACT A general notion of the Allee effect for higher dimensional triangular maps is
proposed. A global dynamics theory is established. The theory is applied to multi-species …

We consider a two-species hierarchical competition model with a strong Allee effect. The
Allee effect is assumed to be caused by predator saturation. Moreover, we assume that there …

In this paper we develop a high order explicit finite difference weighted essentially non-
oscillatory (WENO) scheme for solving a hierarchical size-structured population model with …

In this paper we present a proof of existence and uniqueness of solution for a class of PDE
models of size structured populations with distributed state-at-birth and having nonlinearities …

In this paper we discuss two explicit finite difference schemes, namely a first order upwind
scheme and a second order high resolution scheme, for solving a hierarchical size …

The dynamics of hierarchical competitive metapopulation models are studied where local
population dynamics are topologically conjugate to those of Ricker's or Verhulst's models …

This is part II of an earlier paper that dealt with hierarchical models with the Allee effect but
with no immigration. In this paper, we greatly simplify the proofs in part I and provide a proof …