A <a href="//commons.wikimedia.org/wiki/Dynamical_system" title="Dynamical system">dynamical system</a> is a system that changes over time, and its state at any time is uniquely determined by the initial state. Examples of dynamical systems: the <a href="//commons.wikimedia.org/wiki/Solar_system" class="mw-redirect" title="Solar system">Solar system</a>, consisting of celestial bodies interacting according to the law of universal gravitation, <a href="https://en.wikipedia.org/wiki/https://en.wikipedia.org/wiki/Modelling_biological_systems" class="extiw" title="en:https://en.wikipedia.org/wiki/Modelling biological systems">biological models</a> describing the development of cells, organisms and populations. Quite often, a dynamical system can be described by <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation" class="extiw" title="en:Ordinary differential equation">ordinary differential equations</a>, relating the state of the system with the speed of this state changing. The system evolution can be represented as a curve, every point of which is the state of the system at a certain time (this curve is called the <a href="https://en.wikipedia.org/wiki/Phase_space" class="extiw" title="en:Phase space">phase trajectory</a>). <a href="//commons.wikimedia.org/wiki/Attractor" title="Attractor">Attractor</a> is a set in space of all possible states to which the system approaches when the time tends to infinity. Sometimes, if the system dimension (number of degrees of freedom) is at least 3, its attractors can have rather complex shape. There are some special recipes of building  "multiplied" complex attractors from elementary ones, here is a book dedicated to it: <a rel="nofollow" class="external free" href="http://www.ee.cityu.edu.hk/~gchen/pdf/LC-IJBC06-survey.pdf">http://www.ee.cityu.edu.hk/~gchen/pdf/LC-IJBC06-survey.pdf</a>
<ul><li>7-scroll attractor, p.818</li>
<li>Modified proto-Lorenz system (4 scrolls), p.833</li>
<li>Two-attractor grid multi-scroll chaotic system: <a rel="nofollow" class="external free" href="http://cpb.iphy.ac.cn/EN/article/downloadArticleFile.do?attachType=PDF&amp;id=25178">http://cpb.iphy.ac.cn/EN/article/downloadArticleFile.do?attachType=PDF&amp;id=25178</a></li>
<li>Grid multi-wing butterfly chaotic attractor: <a rel="nofollow" class="external free" href="http://www.mii.lt/na/issues/NA_1902/NA19209.pdf">http://www.mii.lt/na/issues/NA_1902/NA19209.pdf</a></li></ul>
For images preparing it was used following proprietary software: <a rel="nofollow" class="external free" href="http://odestudy.wix.com/derek">http://odestudy.wix.com/derek</a>
<a href="//commons.wikimedia.org/wiki/User:Belch84" title="User:Belch84">Belch84</a>
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