Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChaos synchronization of identical Sprott systems by active control
60
0
0.0
(
0
)
Authors
Marcin Daszkiewicz
Ask ChatGPT about the research
No Arabic abstract
In this article we synchronize by active control method all 19 identical Sprott systems provided in paper [10]. Particularly, we find the corresponding active controllers as well as we perform (as an example) the numerical synchronization of two Sprott-A models.
rate research
Read More
Recently, there has been provided two chaotic models based on the twist-deformation of classical Henon-Heiles system. First of them has been constructed on the well-known, canonical space-time noncommutativity, while the second one on the Lie-algebraically type of quantum space, with two spatial directions commuting to classical time. In this article, we find the direct link between mentioned above systems, by synchronization both of them in the framework of active control method. Particularly, we derive at the canonical phase-space level the corresponding active controllers as well as we perform (as an example) the numerical synchronization of analyzed models.
In this article we provide the noncommutative Sprott models. We demonstrate, that effectively, each of them is described by system of three complex, ordinary and nonlinear differential equations. Apart of that, we find for such modified models the corresponding (noncommutative) jerk dynamics as well as we study numerically as an example, the deformed Sprott-A system.
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables nor it needs to be active for all times for achieving generalized synchronization. The procedure is based on the analogy between a response map subject to an external drive acting with a probability p and an autonomous system of coupled maps where a global interaction between the maps takes place with this same probability. It is shown that, under some circumstances, the conditions for stability of generalized synchronized states are equivalent in both types of systems. Our results reveal the existence of similar minimal conditions for the emergence of generalized synchronization of chaos in driven and in autonomous spatiotemporal systems.
This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state error variables. A sufficient synchronization criterion for a general linear state error feedback controller is rigorously proven by means of linearization and Lyapunovs direct methods. When a simple linear controller is used in the scheme, some easily implemented algebraic synchronization conditions are derived based on the upper and lower bounds of the master chaotic system. These criteria are further optimized to improve their sharpness. The optimized criteria are then applied to four typical generalized Lorenz systems, i.e. the classical Lorenz system, the Chen system, the Lv system and a unified chaotic system, obtaining precise corresponding synchronization conditions. The advantages of the new criteria are revealed by analytically and numerically comparing their sharpness with that of the known criteria existing in the literature.
Chaos synchronization may arise in networks of nonlinear units with delayed couplings. We study complete and sublattice synchronization generated by resonance of two large time delays with a specific ratio. As it is known for single delay networks, the number of synchronized sublattices is determined by the Greatest Common Divisor (GCD) of the network loops lengths. We demonstrate analytically the GCD condition in networks of iterated Bernouilli maps with multiple delay times and complement our analytic results by numerical phase diagrams, providing parameter regions showing complete and sublattice synchronization by resonance for Tent and Bernouilli maps. We compare networks with the same GCD with single and multiple delays, and we investigate the sensitivity of the correlation to a detuning between the delays in a network of coupled Stuart-Landau oscillators. Moreover, the GCD condition also allows to detect time delay resonances leading to high correlations in non-synchronizable networks. Specifically, GCD-induced resonances are observed both in a chaotic asymmetric network and in doubly connected rings of delay-coupled noisy linear oscillators.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
