5 papers · 1 filter
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 formul…
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…
Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients
Cinzia Elia, Roberta Fabbri, Carmen Núñez
Nonautonomous bifurcation theory is a growing branch of mathematics, for the insight it provides into radical changes in the global dynamics of realistic models for many real-world…
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…