Analysis of local dynamics of difference and close to them differential-difference equations
In this paper, by using the asymptotic expansion techniques and bifurcation theory, the authors study the asymptotic properties of the solutions of the differential-difference equation \[ \gamma\mu^3u'''+\frac12\mu^2u''+\mu u'+u=au(t-1)+f(u(t-1)),\;\;t\in[0,\infty), \] analyzing the cases \(0<\gamma\leq 1/8,\) \(1/8<\gamma<1/2\) and \(\gamma=1/2\) separately and where essentially different results are obtained. Here, \(0<\mu,\varepsilon\ll1\) are small parameters, \(a=-(1+\varepsilon a_1)\) and \(f(u)=f_2u^2+f_3u^3+O(u^4).\)
scientific article; zbMATH DE number 7000197