RT info:eu-repo/semantics/article
T1 Critical transitions for asymptotically concave or d-concave nonautonomous differential equations with applications in Ecology
A1 Dueñas, Jesús
A1 Núñez, Carmen
A1 Obaya, Rafael
AB The occurrence of tracking or tipping situations for a transition equation $x'=f(t,x,\G(t,x))$with asymptotic limits $x'=f(t,x,\G_\pm(t,x))$ is analyzed. The approaching condition is just$\lim_{t\to\pm\infty}(\G(t,x)-\G_\pm(t,x))=0$ uniformly on compact real sets, and sothere is no restriction to the dependence on time of the asymptotic equations. The hypothesesassume concavity in $x$ either of the maps $x\mapsto f(t,x,\G_\pm(t,x))$ or of their derivatives with respectto the state variable (d-concavity), but not of $x\mapsto f(t,x,\G(t,x))$ nor of its derivative.}The analysis providesa powerful tool to analyze the occurrence of critical transitions for one-parametricfamilies $x'=f(t,x,\G^c(t,x))$. The new approach significatively widens the fieldof application of the results, since the evolution law of the transitionequation can be essentially different from those of the limit equations.Among these applications, some scalar population dynamics models subjectto non trivial predation and migration patterns are analyzed, both theoretically and numerically.\parSome key points in the proofs are: to understand the transition equationas part of an orbit in its hull which approaches the \upalfa-limit and\upomeg-limit sets; to observe that these sets concentrate all the ergodic measures;and to prove that in order to describe the dynamical possibilities of the equationit is sufficient that the concavity or d-concavity conditions hold for a complete measure subset of theequations of the hull.
PB Springer
YR 2024
FD 2024
LK https://uvadoc.uva.es/handle/10324/69676
UL https://uvadoc.uva.es/handle/10324/69676
LA eng
NO Journal of Nonlinear Science 2024, aceptado
DS UVaDOC
RD 18-nov-2024