2017 CMS Winter Meeting

Waterloo, December 8 - 11, 2017

Dynamical Systems
Org: Sue Ann Campbell and Xinzhi Liu (University of Waterloo)
[PDF]

JACQUES BÉLAIR, Montreal

MONICA COJOCARU, Guelph

WENYING FENG, Trent

MICHAEL LI, Alberta

KYEONGAH NAH, York

MANUELE SANTOPRETE, Wilfrid Laurier University
Mathematical Models of Radicalization  [PDF]

Radicalization is the process by which people come to adopt increasingly extreme political, social, or religious ideologies. In recent years radicalization has become a major concern for national security because it can lead to violent extremism. It is in this context that this talk attempts to describe radicalization mathematically by modelling the spread of extremist ideology as the spread of an infectious disease. This is done by using compartmental epidemiological models. We try to use these models to evaluate the effectiveness of some strategies to counter violent extremism.

GAIL WOLKOWICZ, McMaster

JIANHONG WU, York

YINGFEI YI, University of Alberta
Reducibility of Quasi-Periodic Linear KdV Equation  [PDF]

We consider the following one-dimensional, quasi-periodically forced, linear KdV equations $$u_t+(1+ a_{1}(\omega t,x)) u_{xxx}+ a_{2}(\omega t,x) u_{xx}+ a_{3}(\omega t,x)u_{x} +a_{4}(\omega t,x)u=0$$ under the periodic boundary condition $u(t,x+2\pi)=u(t,x)$, where $\omega$'s are frequency vectors lying in a bounded closed region $\Pi_*\subset R^b$ for some $b>1$, $a_i: T^b\times T\to R$, $i=1,\cdots,4$, are bounded above by a small parameter $\epsilon_*>0$ under a suitable norm, real analytic in $\phi\in T^b$ and sufficiently smooth in $x\in T$, and $a_1,a_3$ are even, $a_2,a_4$ are odd. Under the real analyticity assumption of the coefficients, we show that there exists a Cantor set $\Pi_{\epsilon_*}\subset \Pi_*$ with $|\Pi_*\setminus \Pi_{\epsilon_*}|=O(\epsilon_*^{\frac 1{100}})$ such that for each $\omega\in \Pi_{\epsilon_*}$, the corresponding equation is smoothly reducible to a constant-coefficients one. This problem is closely related to the existence and linear stability of quasi-periodic solutions in a nonlinear KdV equation.

PEI YU, Western

YUAN YUAN, Memorial

XIAOQIANG ZHAO, Memorial University of Newfoundland
Almost Pulsating Waves in Time and Space Periodic Media  [PDF]

In this talk, I will report our recent research on almost pulsating waves for monotone semiflows with monostable structure in time and space periodic media. Our method is a combination of the Poincare maps approach and an evolution viewpoint. The developed theory is then applied to two species competitive reaction-advection-diffusion systems. It turns out that the minimal wave speed exists and coincides with the single spreading speed for such a system no matter whether the spreading speed is linearly determinate. This talk is based on a joint work with Drs. Jian Fang and Xiao Yu.

HUAIPING ZHU, York

XINGFU ZOU, Western

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