25 citations · 76 across the 18 of their papers we have counts for
18 papers
Dichotomies Faster or Slower than exponential are Irrelevant for Skew-Product Flows
Néstor Jara, Iacopo P. Longo, Martin Rasmussen
We prove that dichotomies given by growth rates that are either faster or slower than exponential either do not occur or are inconsequential in the setting of skew-products with co…
Invariant Sets and Boundary Systems of Nonautonomous Differential Inclusions
Konstantinos Kourliouros, Iacopo P. Longo, Martin Rasmussen
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the co…
Nonautonomous modelling in Energy Balance Models of climate. Limitations of averaging and climate sensitivity
Iacopo P. Longo, Rafael Obaya, Ana M. Sanz
Starting from a classical Budyko-Sellers-Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irrad…
Global bifurcation of homoclinic solutions
Iacopo P. Longo, Christian Pötzsche, Robert Skiba
In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient c…
On the transition between autonomous and nonautonomous systems: the case of FitzHugh-Nagumo's model
Iacopo P. Longo, Elena Queirolo, Christian Kuehn
This work deals with a parametric linear interpolation between an autonomous FitzHugh-Nagumo model and a nonautonomous skewed-problem with the same fundamental structure. This para…
Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time
Iacopo P. Longo, Rafael Obaya, Ana M. Sanz
New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quit…
Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology
Jesús Dueñas, Iacopo P. Longo, Rafael Obaya
This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponent…
Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Iacopo P. Longo
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The re…
Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates
Iacopo P. Longo, Carmen Núñez, Rafael Obaya
The global dynamics of a nonautonomous Carathéodory scalar ordinary differential equation , given by a function which is concave in , is determined by the existen…
Topologies of continuity for Carathéodory parabolic PDEs from a dynamical perspective
Iacopo P. Longo, Rafael Obaya, Ana M. Sanz
Systems of non-autonomous parabolic partial differential equations over a bounded domain with nonlinear term of Carathéodory type are considered. Appropriate topologies on sets of…
Critical transitions in piecewise uniformly continuous concave quadratic ordinary differential equations
Iacopo P. Longo, Carmen Núñez, Rafael Obaya
A critical transition for a system modelled by a concave quadratic scalar ordinary differential equation occurs when a small variation of the coefficients changes dramatically the…
Rate-induced tipping and saddle-node bifurcation for a class of quadratic differential equations with nonautonomous asymptotic dynamics
Iacopo P. Longo, Carmen Núñez, Rafael Obaya +1
An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations , where and $p\colon…
Resilience of dynamical systems
Hana Krakovská, Christian Kühn, Iacopo P. Longo
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challengi…
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method
Christian Kuehn, Iacopo P. Longo
The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution wh…
Monotone skew-product semiflows for Carathéodory differential equations and applications
Iacopo P. Longo, Sylvia Novo, Rafael Obaya
The first part of the paper is devoted to studying the continuous dependence of the solutions of Carathéodory constant delay differential equations where the vector fields satisfy…
Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics
Iacopo P. Longo, Sylvia Novo, Rafael Obaya
We study some already introduced and some new strong and weak topologies of integral type to provide continuous dependence on continuous initial data for the solutions of non-auton…
Weak topologies for Carathéodory differential equations. Continuous dependence, exponential Dichotomy and attractors
Iacopo P. Longo, Sylvia Novo, Rafael Obaya
We introduce new weak topologies and spaces of Carathéodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector…
Topologies of type for Carathéodory functions with applications in non-autonomous differential equations
Iacopo P. Longo, Sylvia Novo, Rafael Obaya
Metric topological vector spaces of Carathéodory functions and topologies of type are introduced, depending on a suitable set of moduli of continuity. Theorems of conti…