Some important results on persistence are reviewed. These results concern the behavior of the orbits approaching the boundary. The orbits restrict the flow on the boundary, if one of them approaches more than one invariant set. A typical example is a model for cyclic competition, where the heteroclinic cycle can be the ω-limit set. Thus the persistence can be reduced to some conditions on the boundary flow
AbstractAn acyclicity theorem on uniform persistence is proved for continuous processes. This result...
The concept of persistence plays an important role when modeling various chemical or biological situ...
Abstract. The theory of Lyapunov exponents and methods from ergodic the-ory have been employed by se...
The theme of this paper is the concept of persistence, its types and different properties. Generally...
AbstractGiven an autonomous system with an isolated equilibrium, we consider general periodic pertur...
We prove an algebraic stability theorem for interleaved persistence modules that is more general tha...
International audienceWe address the biological dynamics problem of the persistence of several speci...
We consider a model composed of two patches and analyze two cases. One patch has two competitors in ...
Abstract. Persistence and permanence are properties of dynamical systems that describe the long-term...
Abstract. This paper concerns the long-term behavior of population systems, and in particu-lar of ch...
Abstract. Kolmogorov vector fieldsẋ i = x i f i (x) on the non-negative cone R n + on R n are often ...
The basic ODE models in mathematical ecology take the form ẋi = xifi(x1,..., xn) (i = 1,..., n) (1)...
Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact mani...
AbstractBoth uniform persistence and global extinction are established for two species predator–prey...
Abstract. By appealing to the theory of global attractors on complete metric spaces, we obtain weake...
AbstractAn acyclicity theorem on uniform persistence is proved for continuous processes. This result...
The concept of persistence plays an important role when modeling various chemical or biological situ...
Abstract. The theory of Lyapunov exponents and methods from ergodic the-ory have been employed by se...
The theme of this paper is the concept of persistence, its types and different properties. Generally...
AbstractGiven an autonomous system with an isolated equilibrium, we consider general periodic pertur...
We prove an algebraic stability theorem for interleaved persistence modules that is more general tha...
International audienceWe address the biological dynamics problem of the persistence of several speci...
We consider a model composed of two patches and analyze two cases. One patch has two competitors in ...
Abstract. Persistence and permanence are properties of dynamical systems that describe the long-term...
Abstract. This paper concerns the long-term behavior of population systems, and in particu-lar of ch...
Abstract. Kolmogorov vector fieldsẋ i = x i f i (x) on the non-negative cone R n + on R n are often ...
The basic ODE models in mathematical ecology take the form ẋi = xifi(x1,..., xn) (i = 1,..., n) (1)...
Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact mani...
AbstractBoth uniform persistence and global extinction are established for two species predator–prey...
Abstract. By appealing to the theory of global attractors on complete metric spaces, we obtain weake...
AbstractAn acyclicity theorem on uniform persistence is proved for continuous processes. This result...
The concept of persistence plays an important role when modeling various chemical or biological situ...
Abstract. The theory of Lyapunov exponents and methods from ergodic the-ory have been employed by se...
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