7 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…
Averaging and tracking of local attractors in slowly varying systems with two time scales
Carmen Núñez, Rafael Obaya, Jorge RodrÃguez
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, Rafael Obaya, Ana M. Sanz
The space of parametric b-measures endowed with appropriate topologies is introduced to define a new class of generalized ODEs given by parametric b-measures. This framework offers…
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…