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Dynamics of a model of two delay-coupled relaxation oscillators
Coupled oscillators Devil’s Staircase Delay-differential equations
2015/8/27
This paper investigates the dynamics of a new model of two coupled relaxation oscilla-tors. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach wit...
Anisotropic interactions in a first-order aggregation model:a proof of concept
Anisotropy visual perception aggregation models implicit equations regularization relaxation time uniqueness criteria singular perturbation
2015/7/14
We extend a well-studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modeled by limited sensorial perception of individuals, that depend...
Degenerating the Jacobian: the Néron Model versus Stable Sheaves
N´ eron model stable sheaf compactified Jacobians relative Picard functor
2011/1/21
We provide sufficient conditions for the line bundle locus in a family of compact moduli spaces of pure sheaves to be isomorphic to the N´eron model. The result applies to moduli spaces construc...
A global mathematical investigation of a predator-prey model
predator-prey plane differential system
2010/4/8
We construct a global bifurcation diagram of the plane differential system $$ {l} \dot x = x(1-x)-x y/(a+x^2), \dot y = y(\delta-\beta y/x), x(t)>0, y(t)>0, a>0, \delta>0, \beta>0, $$ which describes ...