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- W1588337788 abstract "AbstracWe study the linear stability of dynamical systems as a function of the number of degrees of freedom and of the fraction of direct couplings, i.e. connectance, among them. It is commonly accepted within the community of dynamical systems that the stability decreases when increasing the number of degrees of freedom or when increasing the connectance. Conversely, ecologists have long sought models such that stability increases with the complexity. After an historical overlook, we show in this paper that both results can be obtained and that they are strictly related to the sign and magnitude of the matrix elements characterizing the linearization of the dynamical system about an equilibrium point. More precisely, systems characterized by negative o?-diagonal coe?cients are shown to display an increased stability at large connectance where the matrix elements fall in suitable ranges. The analytic study of a very speci?c system and the numerical investigation of more generic cases allow us to give new criteria to establish when stability can increase with the connectance." @default.
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- W1588337788 date "2007-12-13" @default.
- W1588337788 modified "2023-09-27" @default.
- W1588337788 title "Connectance and Stability of Dynamical Systems" @default.
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- W1588337788 doi "https://doi.org/10.1007/978-3-540-72984-6_4" @default.
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