Bifurcation theory of attractors and minimal sets in d-concave nonautonomous scalar ordinary differential equations
Jesús García de Dueñas, Carmen Núñez, Rafael Obaya
Abstract
Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the equation and the concavity of its derivative with respect to the state variable. The skewproduct formalism leads to the analysis of the number and properties of the minimal sets and of the shape of the global attractor, whose abrupt variations determine the occurrence of local saddle-node, local transcritical and global pitchfork bifurcation points of minimal sets and of discontinuity points of the global attractor.
Topics & Concepts
MathematicsAttractorMathematical analysisOrdinary differential equationSaddle-node bifurcationTranscritical bifurcationPitchfork bifurcationBifurcation theoryBifurcationInfinite-period bifurcationBifurcation diagramDifferential equationNonlinear systemPhysicsQuantum mechanicsStability and Controllability of Differential EquationsNonlinear Dynamics and Pattern FormationAdvanced Differential Equations and Dynamical Systems