Wild pseudohyperbolic attractor in a four-dimensional Lorenz system. (English) Zbl 1472.34106
The authors consider the 4D extension of the Lorenz system
\begin{align*}
& \dot{x}=\sigma \left( y-x \right), \\
& \dot{y}=x\left( r-z \right)-y, \\
& \dot{z}=xy-bz+\mu w, \\
& \dot{w}=-bw-\mu z, \\
\end{align*}
where \(\sigma ,r,b,\mu \) are system parameters. With the help of numerical experiments, the authors show that the system under consideration has a so-called wild pseudohyperbolic spiral attractor [D. V. Turaev and L. P. Shil’nikov, Sb. Math. 189, No. 2, 137–160 (1998; Zbl 0927.37017); translation from Mat. Sb. 189, No. 2, 291–314 (1998)], that is, pseudohyperbolic, spiral (contains a saddle-focus equilibrium), and wild (contains a hyperbolic set with homoclinic tangencies).
Reviewer: Eduard Musafirov (Grodno)
MSC:
| 34D45 | Attractors of solutions to ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Citations:
Zbl 0927.37017Software:
RODESReferences:
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