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A genetic regulatory network mediated by small RNA with two time delays is investigated. We show by mathematical analysis and simulation that time delays can provide a mechanism for the intracellular oscillator. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations...
By using the method of dynamical systems, this paper researches the bifurcation and the exact traveling wave solutions for a (1+2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Exact parametric representations of all wave solutions are given.
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