17 citations · 56 across the 11 of their papers we have counts for
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Asymptotically Autonomous Maps: Heteroclinic connections, Splitting and Phase-induced tipping
Jesús Dueñas, Arturo Vieiro
We consider discrete-time dynamical systems generated by the iteration of asymptotically autonomous maps, whose asymptotic behavior may be either conservative or dissipative. These…
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…
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…
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…
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…
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 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…
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…