6 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 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 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…
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…