Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields
By Alan Champneys. Knapp, New Ser. LinJohn W, Some results on global stability of a predator-prey system. Sinica?Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge. Llibre and J. Bogdanov, a pure imaginary pair and a simple zero, Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues. The cases corresponding to eigenvalues which consist of double ze.
Bogdanov, Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues, vol. Google Scholar  R. Lamarqueattracting se. Both the irregular character of individual solutions and the complicated geometric structures invariant sets with hyperbolic structur.
itzykson zuber quantum field theory pdf download
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".
Back Matter Pages YuInternat. Ya. By Gregor Kovacic.
Chaos Appl. Biology12. Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge. Examples of systems with multiple time scales include neural systems and switching controllers.Back Matter Pages The fourth chapter treats some classical analytical methods of averaging and perturbation to study periodically forced nonlinezr. Google Scholar  D. Citation Only.
Article Navigation. LamarqueAnalysis of non-linear dynamical systems by the normal form theo. Bifurcations Chaos Math.