اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSimulation studies on the design of optimum PID controllers to suppress chaotic oscillations in a family of Lorenz-like multi-wing attractors
88
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness and hence the complexity of the state time series for these multi-wing chaotic systems is much higher than that of the conventional double-wing chaotic attractors. A real-coded Genetic Algorithm (GA) based global optimization framework has been adopted in this paper as a common template for designing optimum Proportional-Integral-Derivative (PID) controllers in order to control the state trajectories of four different multi-wing chaotic systems among the Lorenz family viz. Lu system, Chen system, Rucklidge (or Shimizu Morioka) system and Sprott-1 system. Robustness of the control scheme for different initial conditions of the multi-wing chaotic systems has also been shown.
قيم البحث
اقرأ أيضاً
This article briefly introduces the generalized Lorenz systems family, which includes the classical Lorenz system and the relatively new Chen system as special cases, with infinitely many related but not topologically equivalent chaotic systems in between.
A generalization of the Lorenz equations is proposed where the variables take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic
fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of $mathfrak{u}(2)$. We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations.
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and Rossler systems as examples. The Schrodinger equation for the corresponding quantum statistical ensemble is described in ter
ms of the Hamilton-Jacobi formalism. We consider both the original dynamical system in the position space and the conjugate dynamical system corresponding to the momentum space. Such simultaneous consideration of mutually complementary position and momentum frameworks provides a deeper understanding of the nature of chaotic behavior in dynamical systems. We have shown that the new formalism provides a significant simplification of the Lyapunov exponents calculations. From the point of view of quantum optics, the Lorenz and Rossler systems correspond to three modes of a quantized electromagnetic field in a medium with cubic nonlinearity. From the computational point of view, the new formalism provides a basis for the analysis of complex dynamical systems using quantum computers.
We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to anot
her basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.
In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then, for a qualit
ative description of the different types of homoclinic bifurcations, a numerical analysis of the detected parameter region is carried out to discover several new interesting bifurcation scenarios.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
