Abstracts - Facultatea de Matematică
Abstracts - Facultatea de Matematică
Abstracts - Facultatea de Matematică
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Posters<br />
On the convergence of solutions to a certain fifth or<strong>de</strong>r<br />
nonlinear differential equation<br />
Olufemi A<strong>de</strong>yinka ADESINA<br />
Department of Mathematics, Obafemi awolowo University, Ile-Ife, Nigeria<br />
oa<strong>de</strong>sina@oauife.edu.ng<br />
In this paper, sufficient conditions for convergence of solutions to the fifth or<strong>de</strong>r<br />
nonlinear differential equation:<br />
x (v) + ax (iv) + bx ′′′ + cx ′′ + g(x ′ ) + h(x) = p(t, x, x ′ , x ′′ , x ′′′ , x (iv) ),<br />
in which a, b and c are positive constants, functions h(x) and p(t, x, x ′ ,<br />
x ′′ , x ′′′ , x (iv) ) are real valued and continuous in their respective arguments are obtained.<br />
The function h(x) is not necessarily differentiable but satisfies an incrementally ratio<br />
h(ζ + η) − h(ζ)<br />
η<br />
where I0 is a closed Routh–Hurwitz interval.<br />
∈ I0, η �= 0,<br />
Competition in patchy space with cross diffusion and toxic<br />
substances<br />
Shaban ALY<br />
Department of Mathematics, Faculty of Science, Al-Azhar University<br />
Assiut 71511, Egypt<br />
shhaly12@yahoo.com<br />
In this paper we formulate a Lotka-Volterra competitive system affected by toxic<br />
substances in two patches in which the per capita migration rate of each species is<br />
in.uenced not only by its own but also by the other one.s <strong>de</strong>nsity, i.e. there is cross<br />
diffusion present. Numerical studies show that at a critical value of the bifurcation<br />
parameter the system un<strong>de</strong>rgoes a Turing bifurcation and the cross migration response<br />
is an important factor that should not be ignored when pattern emerges.<br />
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