25 citations · 190 across the 38 of their papers we have counts for
40 papers
Loss-of-hyperbolicity and jump bifurcations in scalar nonautonomous d-concave ODEs
Jesús Dueñas, Carmen Núñez, Rafael Obaya
The paper studies bifurcation for additively parametrized scalar nonautonomous ODEs of the form , where is d-concave and coercive in the state variable. By formula…
Averaging and tracking of local attractors in slowly varying systems with two time scales
Carmen Núñez, Rafael Obaya, Jorge Rodríguez
The paper analyzes to what extent the dynamics of a nonautonomous -dimensional dynamical system with two time scales, formulated in the slow time as $dx/dt=f(t/\varepsilon, t, x…
A new class of generalized ordinary differential equations with applications
Sylvia Novo, Iacopo P. Longo, Rafael Obaya +1
The paper presents a new approach to the study of precompact families of Carathéodory ODEs using techniques from nonautonomous dynamical systems, together with some applications.
Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence
Jesús Dueñas, Carmen Núñez, Rafael Obaya
The long-term dynamics of a Bonifacio-Lugiato model of optical superfluorescence is investigated. The scalar ordinary differential equation modelling the phenomenon is given by a c…
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…
Concave-convex nonautonomous scalar ordinary differential equations: from bifurcation theory to critical transitions
Jesús Dueñas, Carmen Núñez, Rafael Obaya
A mathematical modeling process for phenomena with a single state variable that attempts to be realistic must be given by a scalar nonautonomous differential equation t…
Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits
Jesús Dueñas, Carmen Núñez, Rafael Obaya
Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations sa…
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…
Exponential Ordering for Nonautonomous Neutral Functional Differential Equations
Sylvia Novo, Rafael Obaya, Víctor M. Villarragut
We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the expone…
Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator
Rafael Obaya, Víctor M. Villarragut
We study neutral functional differential equations with stable linear non-autonomous -operator. The operator of convolution transforms into . We show that, if…
Neutral Functional Differential Equations with Applications to Compartmental Systems
Víctor Muñoz-Villarragut, Sylvia Novo, Rafael Obaya
We study the monotone skew-product semiflow generated by a family of neutral functional differential equations with infinite delay and stable D-operator. The stability properties o…
Critical Transitions for Asymptotically Concave or D-Concave Nonautonomous Differential Equations with Applications in Ecology
Jesús Dueñas, Carmen Núñez, Rafael Obaya
The occurrence of tracking or tipping situations for a transition equation is analyzed under the assumptions on concavity in either of the maps giving rise t…
Two dynamical approaches to the notion of exponential separation for random systems of delay differential equations
Marek Kryspin, Janusz Mierczynski, Sylvia Novo +1
This paper deals with the exponential separation of type II, an important concept for random systems of differential equations with delay, introduced in \JM\ et al.~\cite{MiNoOb1}.…
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…
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…
Critical Transitions in D-Concave Nonautonomous Scalar Ordinary Differential Equations Appearing in Population Dynamics
Jesús Dueñas, Carmen Núñez, Rafael Obaya
A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous c…
Uniform stability and chaotic dynamics in nonhomogeneous linear dissipative scalar ordinary differential equations
Juan Campos, Carmen Nuñez, Rafael Obaya
The paper analyzes the structure and the inner long-term dynamics of the invariant compact sets for the skewproduct flow induced by a family of time-dependent ordinary differential…
The exponential ordering for non-autonomous delay systems with applications to compartmental Nycholson systems
Sylvia Novo, Rafael Obaya, Ana M. Sanz +1
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Som…
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…
Generalized Pitchfork Bifurcations in D-Concave Nonautonomous Scalar Ordinary Differential Equations
J. Dueñas, C. Núñez, R. Obaya
The global bifurcation diagrams for two different one-parametric perturbations ( and ) of a dissipative scalar nonautonomous ordinary differential equation …
Bifurcation Theory of Attractors and Minimal Sets in D-Concave Nonautonomous Scalar Ordinary Differential Equations
J. Dueñas, C. Núñez, R. Obaya
Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the…
New notion of nonuniform exponential dichotomy with applications to the theory of pullback and forward attractors
Jose Antonio Langa, Rafael Obaya, Alexandre N. Oliveira-Sousa
In this work we study nonuniform exponential dichotomies and existence of pullback and forward attractors for evolution processes associated to nonautonomous differential equations…
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…