Nonlinear oscillations dynamical systems and bifurcations of vector fields pdf
Download Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector FieldsHe 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". Examples of systems with multiple time scales include neural systems and switching controllers.
Introducing Bifurcations: The Saddle Node Bifurcation
Download Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields 1983
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Koon, M. Lo, J. Marsden and S. Chapter 2 Chapter 6 Chapter 7 References on periodic orbits and their computation Divakar Viswanath  The Lindstedt-Poincare technique as an algorithm for computing periodic orbits. SIAM Review 43 3 ,
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