اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the behaviour of solutions to discrete time Lotka-Volterra equation
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The time evolution of a class of completely integrable discrete Lotka-Volterra s ystem is shown not unique but have two different ways chosen randomly at every s tep of generation. This uncertainty is consistent with the existence of constant s of motion and disappears in both continuous time and ultra discrete limits.
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This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system begin{equation}label{eq:abstract} begin{cases} u_{t}= u_{xx} + u(1-u-av), & qquad xinmathbb{R} cr v_{t}= d v_{xx}+ rv(1-v-bu), & qquad
xinmathbb{R} end{cases} quad (1) end{equation} where $d,r,a$, and $b$ are positive constants with $a eq 1$ and $b eq 1$. We prove the existence of some entire solutions $(u(t,x),v(t,x))$ of $(1)$ corresponding to $(Phi_{c}(xi),0)$ at $t=-infty$ (where $xi=x-ct$ and $Phi_c$ is a traveling wave solution of the scalar Fisher-KPP defined by the first equation of $(1)$ when $a=0$). Moreover, we also describe the asymptotic behavior of these entire solutions as $tto+infty$. We prove existence of new entire solutions for both the weak and strong competition case. In the weak competition case, we prove the existence of a class of entire solutions that forms a 4-dimensional manifold.
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Let the population of e.g. a country where some opinion struggle occurs be varying in time, according to Verhulst equation. Consider next some competition between opinions such as the dynamics be described by Lotka and Volterra equations. Two kinds o
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