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[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Bourama Toni (Virginia State University)
April 17, 2015
2pm - 3pm
Abstract
We develop the concept of Quasi and p-Adic Limit Cycles at the interface between the theories of limit cycles and quasi periodicity to include almost and pseudo-almost periodicity, almost automorphy, and p-Adic almost periodicity, in both the usual Archimedean metric spaces and the p-Adic (ultrametric) spaces.
We investigate the conditions of existence and uniqueness, stability and bifurcation, as well as the notion of quasi-isochrons. Illustrative examples include perturbations of the Poincare oscillator and the Lienard systems under various external forcing, with applications to quasi-periodic solitary waves uncovered by transforming some hyperbolic and reaction-diffusion PDE into forced Lienard systems.
Also presented is on-going research on the co-existence of limit cycles and strictly quasi limit cycles, the existence of quasi isochronous limit cycles, and most importantly the transition to chaotic behavior, possibly through coupling/synchronization of quasi oscillators (e.g., forced Master-Slave systems).
Bio-Sketch: Dr. Bourama Toni
A graduate of University of Montreal, Canada, Dr. Bourama Toni is a Full Professor of Mathematics at Virginia State University, Petersburg VA. His Research Interests are in Differential Analysis, Archimedean and p-Adic Dynamical Systems and their Applications, to include: Bifurcation of Critical Periods and Isochronous Systems, in particular Limit Cycles and Quasi Limit Cycles; Evolution Equations in Banach and Hilbert Spaces, in particular Almost, Pseudo Almost and Almost Automorphic Periodicity; Evolutionary Game Theory; Feedback Loops Analysis in Physical and Life Sciences; these interests have expanded into Mathematics and Arts (Paintings with Proses with first Solo Exhibition of 55 pieces in Fall 2014).
Dr. Toni also manages the on-going interdisciplinary STEAM-H intensive seminar series, editing the books of proceedings in the SPRINGER PROMS series, currently in its 4th Volume.
We develop the concept of Quasi and p-Adic Limit Cycles at the interface between the theories of limit cycles and quasi periodicity to include almost and pseudo-almost periodicity, almost automorphy, and p-Adic almost periodicity, in both the usual Archimedean metric spaces and the p-Adic (ultrametric) spaces.
We investigate the conditions of existence and uniqueness, stability and bifurcation, as well as the notion of quasi-isochrons. Illustrative examples include perturbations of the Poincare oscillator and the Lienard systems under various external forcing, with applications to quasi-periodic solitary waves uncovered by transforming some hyperbolic and reaction-diffusion PDE into forced Lienard systems.
Also presented is on-going research on the co-existence of limit cycles and strictly quasi limit cycles, the existence of quasi isochronous limit cycles, and most importantly the transition to chaotic behavior, possibly through coupling/synchronization of quasi oscillators (e.g., forced Master-Slave systems).
Bio-Sketch: Dr. Bourama Toni
A graduate of University of Montreal, Canada, Dr. Bourama Toni is a Full Professor of Mathematics at Virginia State University, Petersburg VA. His Research Interests are in Differential Analysis, Archimedean and p-Adic Dynamical Systems and their Applications, to include: Bifurcation of Critical Periods and Isochronous Systems, in particular Limit Cycles and Quasi Limit Cycles; Evolution Equations in Banach and Hilbert Spaces, in particular Almost, Pseudo Almost and Almost Automorphic Periodicity; Evolutionary Game Theory; Feedback Loops Analysis in Physical and Life Sciences; these interests have expanded into Mathematics and Arts (Paintings with Proses with first Solo Exhibition of 55 pieces in Fall 2014).
Dr. Toni also manages the on-going interdisciplinary STEAM-H intensive seminar series, editing the books of proceedings in the SPRINGER PROMS series, currently in its 4th Volume.
Contact
Junping Shi