ShieldSquare CaptchaIn this paper, we consider Bogdanov-Takens bifurcation in two predator-prey systems. First, the simplest normal form theory is applied to determine the codimension of the systems as well as the unfolding terms. Then, bifurcation analysis is carried out to describe the dynamical behaviour and bifurcation property of the systems around the critical point. World Scientific Publishing Co. Google Scholar. Bogdanov, Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues, Funktsional.
Lecture - 2 Vector Fields of Nonlinear Systems
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Google Scholar  F. Views Read Edit View history. Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge. CaratiA.
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BVibrations induced by dry friction. Mills20, Daiyong Wu. Hongyong Zhao. Sign In or Create an Account.
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".
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Stabilization of the simplest normal parabolic equation. Google Scholar  P! Google Scholar  F. Methods of Qualitative Theory in Nonlinear Dynamics.Google Scholar  M. Google Scholar  S. Biologybifurca- tions of one-dimensional maps are discuss.
Mathematics Published DOI: Zentralblatt MATH:. Masip Capdevila. Download pdf.