We investigate the existence, uniqueness and Gaussian curvature of the invariant carrying
simplices of 3 species autonomous totally competitive Lotka–Volterra systems. Explicit …

This paper is devoted to show that Hirsch's results on the existence of a carrying simplex are
a powerful tool to understand the dynamics of Kolmogorov models. For two and three …

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 develop a notion of monotonicity for maps defined on Euclidean spaces R+ k, of arbitrary
dimension k. This is a geometric approach that extends the classical notion of planar …

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 …

For a C 1 map T from C=[0,+∞) N to C of the form T i (x)= xifi (x), the dynamical system x (n)=
T n (x) as a population model is competitive if∂ fi∂ xj≤ 0 (i≠ j). A well know theorem for …

Carrying Simplices in Discrete Competitive Systems and Age-structured Semelparous
Populations Page 1 Carrying Simplices in Discrete Competitive Systems and Age-structured …

This paper deals with global asymptotic behaviour of the dynamics for N-dimensional
competitive Kolmogorov differential systems of equations $\frac {\mathrm {d}{x} _ {i}}{\mathrm …

We consider a C 1, α smooth flow in R d which is “strongly monotone” with respect to a cone
C of rank k, a closed set that contains a linear subspace of dimension k and no linear …

We investigate the global dynamics from a measure-theoretic perspective for smooth flows
with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently …