Avoiding extremes using partial control. Issue 2 (1st February 2016)

• Record Type: Journal Article
• Authors: Das, Suddhasattwa; Yorke, James
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 2(2016)
• Page Start: 217
• Page End: 234
• Publication Date: 2016-02-01
• Subjects: partial control -- chaotic systems -- safe sets; 93Cxx; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2015.1079181
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : Dynamical systems can be prone to severe fluctuations due to the presence of chaotic dynamics. This paper explains for a toy chaotic economic model how such a system can be regulated by the application of relatively weak control to keep the system confined to a bounded region of the phase space, even in the presence of strong external disturbances. Since the control here is weaker than the disturbance, the system cannot be controlled to a particular trajectory, but under certain circumstances it can be partially controlled to avoid extreme values. Partial control depends on the existence of a certain set called a 'safe sets'. We describe the safe set and how it varies with parameters, sometimes continuously and sometimes discontinuously.