{"id":6528,"date":"2026-06-20T17:33:22","date_gmt":"2026-06-20T09:33:22","guid":{"rendered":"\/jase\/?post_type=tkuisotope&p=6528"},"modified":"2026-08-21T15:38:21","modified_gmt":"2026-08-21T07:38:21","slug":"equilibrium-stabilization-method-to-control-chaotic-behavior-of-continuous-systems","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=equilibrium-stabilization-method-to-control-chaotic-behavior-of-continuous-systems","title":{"rendered":"Equilibrium Stabilization Method to Control Chaotic Behavior of Continuous Systems"},"content":{"rendered":"\n
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<\/i> 2019<\/a><\/p>\n<\/div>\n\n\n\n

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<\/i> Volume 22, Issue 1<\/a><\/p>\n<\/div>\n\n\n\n

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Behnam Babaei and Masoud Shafiee<\/i><\/a><\/p>\n\n\n\n

Department of Electrical Engineering, Amirkabir University of Technology, Iran<\/p>\n<\/div>\n\n\n\n

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Received:\u00a0January 26, 2018
Accepted:\u00a0October 2, 2018
Publication Date:\u00a0June 20, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n

\"\u4e0a\u50b3\u5716\u7247\"\n\n\n

The chaotic behavior of the Lorenz system with initial point(10,5,3). (a) x1<\/sub>, x2<\/sub> and x3<\/sub> are unstablevs.time. (b) The trajectory attractton one of fixed points. This system has three fixed points as listed in Table1.<\/p>\n<\/div>\n<\/div>\n\n\n\n

<\/i> Copyright <\/strong>The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n

Download Citation:  BibTeX <\/a>| http:\/\/dx.doi.org\/10.6180\/jase.201903_22(1).0020<\/a>  <\/p>\n\n\n\n

Download PDF<\/a><\/p>\n\n\n\n

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Chaos is a complicated phenomenon in nonlinear dynamical systems. A dynamic controller, based on the stability transformation method (STM), has been used to stabilize both multiple fixed points and unknown unstable periodic orbits (UPOs) in dynamical systems. However, in these methods, there is not any unified algorithm in order to stabilize the fixed points. Here, we present a universal and simple chaos control algorithm called method of selecting an unstable fixed point (SUFP), which is able to stabilize unstable selected fixed points, by generating a stability matrix. Although this algorithm modifies a system by applying an input feedback, the designed feedback does not relocate the positions of fixed points but changes their stabilities. Results show that all tested chaotic trajectories are attracted to selected points, independent of initial values.<\/p>\n\n\n\n

Keywords:\u00a0<\/em> Stability Matrix, Chaotic System, Fixed Point, Selecting Unstable Fixed Point, SUFP, Eigenvalue, Algorithm, Lorenz Model<\/em><\/p>\n\n\n\n

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