![]() ![]() Zheng, “ Symbolic dynamics for the Lozi map,” Chaos, Solitons Fractals 1, 243 (1991). Chang, “ Boundary influence on the entropy of a Lozi-type map,” J. Holmgren, A First Course in Discrete Dynamical Systems ( Springer, New York, 1996), p. Devaney, An Introduction to Chaotic Dynamical Systems ( Addison-Wesley, Colorado, 2003), p. Abbott, “ Asymmetry and disorder: A decade of Parrondo's paradox,” Fluct. Chaos theory is a scientific principle describing the unpredictability of systems. Salas, “ Dynamic Parrondo's paradox,” Physica D 218, 177 (2006). Toral, “ Capital redistribution brings wealth by Parrondo's paradox,” Fluct. A new research direction in the field of applied chaos technology not only includes controlling chaos, which means to weaken or completely suppress chaos when. Chaos theory is an important aspect of non-linear research, and has infiltrated a number of disciplines and engineering fields. Tamarkin, “ Switching investments can be a bad idea when Parrondo's paradox applies,” J. Danca, “ Deterministic and random synthesis of discrete chaos,” Appl. Dynamical Analysis, Electronic Circuit Design and Control Application of a Different Chaotic System. Adaptive control and adaptive synchronization of such a system with parabolic equilibrium are also reported in Sections 5 and 6. ![]() Islam, “ Randomly chosen chaotic maps can give rise to nearly ordered behavior,” Phys. Yang, “ An example of realizing “order + order = chaos” via synchronization,” Acta Phys. Liu, “ From chaos to order via synchronization,” Commun Appl. The problem of the parametric suppression of chaos in a dynamical system is solved by methods of the optimum control theory. Abbott, “ Control systems with stochastic feedback,” Chaos 11, 715 (2001). Abbott, “ New paradoxical games based on Brownian ratchets,” Phys. Abbott, “ Losing strategies can win by Parrondo's paradox,” Nature 402, 864 (1999). ![]() Romera, “ Can two chaotic systems give rise to order,” Phys. Numerical and mathematical analysis prove that the paradoxical phenomenon of “chaos + chaos = order” also exist in the dynamics generated by non-Mandelbrot maps. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m ( m ≥ 2 ) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Some problems left over in the current literatures are solved. The chaotic maps in our study are more general than those in the current literatures as far as “chaos + chaos = order” is concerned. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. In contrast with other chaos control procedures like the map-based Ott, Grebogi, and York method, the continuous type feedback control proposed by Pyragas, or the feedback control method recently proposed by Brown and Rulkov, the procedure outlined in this paper automatically results in a choice for the feedback gains that gives optimum performance, i.e., minimum fluctuations around the desired trajectory using minimum control actions.This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. This model is used as an observer, i.e., it is synchronized with the experimental pendulum to estimate the state of the experimental pendulum. ![]() possible to improve the predictability of the time series and even to control or. Ogorzalek M.J.(1997A) Chaos and Complexity in Nonlinear Electronic Circuits. Cambridge Core - Differential and Integral Equations, Dynamical Systems and Control Theory - Stability, Instability and Chaos. Chaos theory refers to the behaviour of certain deterministic nonlinear. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical. It is thus shown that linear control methods can be applied to experimental chaotic systems, as long as an adequate model is available that can be linearized along the desired trajectory. Selected Chapters in Automatic Control Theory. That is, both the fluctuations around the target trajectory and the necessary control actions are minimized using a least-squares solution of the linearized problem. About Chaos theory and chaotic systems, Recent developments in chaos-based engineering applications, Chaos in finance and blockchain, Fractional-order. MPC enables tuning of the controller to give an optimal controller performance. Linear feedback control, specifically model predictive control (MPC), was used successfully to synchronize an experimental chaotic pendulum both on unstable periodic and aperiodic orbits. ![]()
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