Abstract:In this paper, we investigate the explicit solutions and stability properties of certain continuous-time homogeneous polynomial dynamical systems via tensor algebra. In particular, if a system of homogeneous polynomial differential equations can be represented by an orthogonal decomposable tensor, we can write down its explicit solution in a simple fashion by exploiting tensor Z-eigenvalues and Z-eigenvectors. In addition, according to the form of the explicit solution, we explore the stability properties of t… Show more
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