Nonlinear oscillations dynamical systems and bifurcations of vector fields pdf

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nonlinear oscillations dynamical systems and bifurcations of vector fields pdf

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields | SpringerLink

Virgin, L. October 1, Guckenheimer and P. Nonlinear Dynam. October ; 1 4 : —
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Introducing Bifurcations: The Saddle Node Bifurcation

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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".

Skip to main content Skip to table of contents. Advertisement Hide. Front Matter Pages i-xvi. Introduction: Differential Equations and Dynamical Systems. Pages An Introduction to Chaos: Four Examples.

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