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Mod-01 Lec-10 Elementary bifurcations
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American Institute of Mathematical Sciences! Dario BambusiA. Google Scholar  V. The analysis is restricted to one-parameter codimension one bifurcations of equilibria.YuFormal decomposition method and parametric normal form. Google Scholar  M. Stabilization of the simplest normal parabolic equation. By Gregor Kovacic.
The mathematical models considered are confined to sets of nonlinear ordinary differential equations and nonlinear maps arisen from their discretizations on finite dimensional Euclidean manifolds. Guckenheimer studies dynamical models of a small neural system, the stomatogastric ganglion of crustaceans - attempting to learn more about neuromodulation. In other projects Wikimedia Fo. Applications mainly drawn from nonlinear oscillations.
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK Nonlinear Oscillations.
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He was previously at the University of California at Santa Cruz John Guckenheimer's research has focused on three areas - neuroscience , algorithms for periodic orbits , and dynamics in systems with multiple time scales. Guckenheimer studies dynamical models of a small neural system, the stomatogastric ganglion of crustaceans - attempting to learn more about neuromodulation , the ways in which the rhythmic output of the STG is modified by chemical and electrical inputs. Employing automatic differentiation , Guckenheimer has constructed a new family of algorithms that compute periodic orbits directly. His research in this area attempts to automatically compute bifurcations of periodic orbits as well as "generate rigorous computer proofs of the qualitative properties of numerically computed dynamical systems". Guckenheimer's research in this area is aimed at "extending the qualitative theory of dynamical systems to apply to systems with multiple time scales".