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In this paper an operable, universal and simple theory on the attractiveness of the invariant manifolds of the two-dimensional dynamical systems is first obtained. It is motivated by the Lyapunovdirect method. It means that for any point in the invariant manifold $M$, $n(\overrightarrow{x})$ is the normal passing by $\overrightarrow{x}$, and $\for all \overrightarrow{x^{'}}\in n(\overrightarrow{x})$,...
In this paper, the dynamics of the coupled Lorenz-Rössler systems with the unidirectionally and the bidirectionally linear coupling are considered. The results show that not only the non-chaotic behaviors appear, but also the region for the chaotic behaviors can increase greatly because of the unidirectionally linear coupling. And the codimension-2 bifurcations can be born because of the bidirectionally...
In this paper, dynamics of the delayed Internet TCP-RED congestion control model is considered employing the analysis software of the delayed dynamical systems-DDE-BIFTOOL. The transmission delay τ1 can make it subject to Hopf and Fold bifurcation, thus the averaged queue length and arrival rate would be the approximately constant or vary periodically. The important effects of the transmission delay...
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