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| In this talk, we numerically study the asymptotic stability of travelling wave solutions for Nicholson's Blowflies equation, a time-delayed reaction diffusion equation, with local or nonlocal nonlinearity.
It is known that, when the ratio of birth rate coefficient and death rate coefficient $p/d$ lies between 1 and $e$, the equation is monotone and possesses monotone traveling wave solutions. However, when the rate is larger than $e$, the equation losses its monotonicity and may possess non-monotone traveling waves when the delay time $r$ is large, which causes the study of stability of these non-monotone traveling waves to be challenging. In this talk, for the case $p/d$ lies between e and $e^{2}$, we numerically show that monotone and non-monotone travelling waves are exponentially stable. For the case that $p/d$ is larger than $e^{2}$, monotone or non-monotone travelling waves are exponentially stable for some small delay time, and are unstable for large delay time. Several interesting numerical results will be demonstrated too.
Joint work with Ming Mei, Chi-Kun Lin and Yanping Lin. |
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