Publisher Summary This chapter discusses a restricted but useful class of dynamical
systems—, namely, those enjoying a comparison principle with respect to a closed order …

It is well known that for the two species autonomous competitive Lotka-Volterra model with
no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst …

The following conjecture of ML Zeeman is proved. If three interacting species modeled by a
competitive Lotka--Volterra system can each resist invasion at carrying capacity, then there …

Let $(X_t) _ {t\geq 0} $ be a continuous time Markov process on some metric space $ M, $
leaving invariant a closed subset $ M_0\subset M, $ called the {\em extinction set}. We give …

In this paper we exploit the linear, quadratic, monotone and geometric structures of
competitive Lotka-Volterra systems of arbitrary dimension to give geometric, algebraic and …

We study the asymptotic behavior of the competitive Leslie/Gower model (map) T: R^ n_+ →
R^ n_+,\quad T_i (x)= c_ix_i 1+ ∑ _ j= 1^ nb_ ij x_j,\quad c_i> 1, b_ ij> 0,\; i, j= 1, ..., n. T: R+ …

We study the dynamics of the multi-species Ricker model given by the map T: R+ n→ R+ n
defined by T i (x)= xi exp ν i 1−∑ j= 1 n μ ijxj, ν i, μ ij> 0, i, j= 1,…, n. It is known that under …

Full article: On existence and uniqueness of the carrying simplex for competitive dynamical
systems Skip to Main Content Taylor and Francis Online homepage Taylor and Francis Online …

In the existing literatures, there exist at least four limit cycles for 3D Lotka-Volterra
competitive systems in Zeeman's classes 26 and 27 with no explicit critical parameter …

We concentrate on the effects of heteroclinic cycles and the interplay of heteroclinic
attractors or repellers on the boundary of the carrying simplices for low-dimensional discrete …