# Introduction to Chaos Control: An Interdisciplinary Problem

• Ricardo Femat
• Gualberto Solis-Perales
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 378)

## Chaos Control Is Suppression or Synchronization

The foundational for chaos control problem is scientific as well as technological. In regard science, on the one hand, chaos control has two important contributions: (i) The controlled chaotic systems has allowed to understand that structured disorder and its entropy/information relationship extend the concept of determinism [1], [2] and (ii) departing from chaotification (inverse action of the chaos suppression) some questions have been opened on phenomena of the feedback dynamical systems [3]. Moreover, the chaos control impacts biomedical, life and engineering sciences; for example, it can be extended to control pathological rhythm in heart [4]. Now, regarding technological applications, the controlled chaotic systemsare important because of a desired frequency response can be induced. Nowadays, the scientific community has identified two problems in chaos control: suppression and synchronization. Among others, we can mention studies in physical devices (e.g., telescopes or lasers), biology/ecology (e.g., population dynamics or biodynamics) or biomedical systems (e.g., heart rhythm or brain activity). Thus, for instance, controlled current-modulation can be entered as excitation from a nonlinear circuit into semiconductors lasers by feeding back the laser frequency response (see Figure 1 in [5]). Henceforth, scientific community has taken possession of the challenge of exploring control techniques such that (i) a family of driving force can command classes of chaotic systems [6], (ii) the synthesis of mathematical expressions for the control force accounts the frequency response [7], and (iii) energy requirements by the control force are accounted (for example to avoid saturation or deterioration in control devices) [8]. In addition, the mathematical models of the driving force is desired to be simple and easy to implement experimentally. A simple form is the linear models of driving forces; which can be expressed in the frequency (Laplace) or time domain and they have been already used to suppress chaotic behavior [7], [9].

## Keywords

Chaotic System Control Force Chaotic Oscillator Generalize Synchronization Chaos Control
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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