Showing papers on "Autonomous system (mathematics) published in 1980"
TL;DR: The informal invitation to participate in this conference included a suggestion that I should try to say something about the possible relationship between chaos in Hamiltonian systems and the chaos associated with strange attractors as discussed by the authors.
Abstract: The informal invitation to participate in this conference included a suggestion that I should try to say something about the possible relationship between chaos in Hamiltonian systems and the chaos associated with strange attractors. I should have refused at once, but i t seems that pride does go before a fall, and I am, after all, making the attempt. All I have managed to accomplish toward providing what seemed wanted was to investigate systems of equations that exhibit both phenomena according to the parameter values they are assigned and, to some extent, the initial conditions. In what follows, I outline some qualitative notions about such systems and raise a few questions about their possible significance.
9 citations
8 citations
01 Jan 1980
TL;DR: It is shown that the linearity restrictions in the theorem of Laroque can be relaxed.
Abstract: nSYMPTOTIC STABILITY OF n SOLUTION OF AN AUTONOMOUS SYSTEM IN m , CONSISTING OF SUBSYSTEMS by Paul van den Heuvel In this paper a generalization is proved of a theorem by Laroque (1979) • • This theorem asserts that if an autonomous system x = F(x) consists of linear subsystems defined on cones in m2 and if the function F(x) is continuous, then the origin is an asymptotically stable solution of the 2 system, if the subsystems are asymptotically stable in m • It is shown that the linearity restrictions in the theorem of Laroque can be relaxed. in a neighbourhood of the equilibrium.
1 citations