Tomberg, Eh. A.; Yakubovich, V. A. Conditions of auto-oscillations in nonlinear systems. (Russian) Zbl 0685.34037 Sib. Mat. Zh. 30, No. 4(176), 180-194 (1989). The authors derive the conditions of auto-oscillations of \(\sigma\) (t) in the system \(dx/dt=Ax+b\xi,\) \(\sigma =c^*x\), \(\xi =\phi (\sigma)\), where A, b, c are real constant matrices, \(x\in {\mathbb{R}}^ n\), \(\sigma \in {\mathbb{R}}^{\ell}\), \(\xi \in {\mathbb{R}}^ m\), \(c^*\) is the conjugate matrix to c, \(\phi \in C^ 1\) is a nonlinear vector function. As an example there are given auto-oscillations in biological systems. Reviewer: P.Marusciak Cited in 1 ReviewCited in 5 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:auto-oscillations; example; biological systems PDFBibTeX XMLCite \textit{Eh. A. Tomberg} and \textit{V. A. Yakubovich}, Sib. Mat. Zh. 30, No. 4(176), 180--194 (1989; Zbl 0685.34037) Full Text: EuDML