Suppressing chaos in continuous systems by impulse control

A new feedback control of a modified Chua's circuit system

In this paper, the fault detection problem for a class of switched nonlinear systems with unknown functions is solved. First, the unknown internal dynamics are approximated by the radial basis function neural networks due to their powerful approximation capabilities. Then, a switched nonlinear observer is developed. Based on the observer, a fault detection scheme is set up with a switched fault detection threshold instead of a common threshold. At the same time, the boundedness of all the signals in the closed-loop system can be guaranteed by using the average dwell time method. Moreover, the fault detection threshold is dependent on the average dwell time, which implies that the fault sensibility can be improved to a certain extent by selecting the average dwell time. Finally, a simulation example on the Chua's circuit system are employed to show the effectiveness of the proposed scheme.

In this paper we will made a study of the dynamics of Chua's circuit system from the Hamilton-Poisson geometry point of view. Using MAPLE 15 it is analyzed the phase portrait for some specific values of parameters.

A robust image encryption algorithm based on Chua's circuit and compressive sensing

Bifurcations and the structure of limit sets are studied for a three-dimensional Chua's circuit system with a cubic nonlinearity. On the base of both computer simulations and theoretical results a model map is proposed which allows one to follow the evolution in the phase space from a simple (Morse-Smale) structure to chaos. It is established that the appearance of a complex, multistructural set of double-scroll type is stimulated by the presence of a heteroclinic orbit of intersection of the unstable manifold of a saddle periodic orbit and unstable manifold of an equilibrium state of saddle-focus type.

The evolution of the target system (leader) in pinning-controlled complex networks may need to be regulated by some control inputs for performing various practical tasks, e.g., obstacle avoidance, tracking highly maneuverable target, and so on. Motivated by this observation, we shall investigate the global pinning synchronization problems for complex switching networks for which the target system is subject to nonzero control inputs. First, using the idea of unit vector function method, a discontinuous coupling law is designed. With the aid of stability theory for switched systems, it is theoretically shown that synchronization in the network under this discontinuous coupling law can be achieved by choosing sufficiently large coupling strengths if the average dwell time (ADT) is bounded below by a positive constant. Second, we use the boundary layer method to design a continuous-coupling law. It has been theoretically shown that the synchronization error is ultimately uniformly bounded (UUB) under this continuous-coupling law. The chattering effect is also avoided in real implementation by using this continuous-coupling law. Furthermore, for networks with unknown external disturbances and unmodeled dynamics, neuro-adaptive-based coupling laws are designed to ensure that the synchronization error of the networks with undirected switching communication topologies under these laws is UUB. The obtained theoretical results are finally validated by performing numerical simulation on coupling Chua's circuit systems.

This study investigates the problem of fault detection (FD) filter design for a class of uncertain Lipschitz systems with time delays, unknown faults, parameter uncertainties and bounded disturbances. A novel FD filter is proposed and the augmented filter system is converted to a linear parameter varying (LPV) system by the reformulated Lipschitz property. Then, two bounded real lemmas (BRLs) are given for the generated residual signal to achieve the fault sensitivity performance in low-/middle-/high-frequency domains and disturbance attenuation performance in the full-frequency domain. Next, the obtained BRLs are further converted into a set of linear matrix inequalities (LMIs) to implement the filter design. Finally, two illustrative simulations including a numerical example and Chua's circuit system clearly demonstrate the advantages of the developed FD scheme.

Understanding synchronization from simple core of chaotic equation

This paper presents a general synchronization technique and an amplitude modulation of chaotic generators. Conventional synchronization and antisynchronization are considered a very narrow subset from the proposed technique where the scale between the output response and the input response can be controlled via control functions and this scale may be either constant (positive, negative) or time dependent. The concept of the proposed technique is based on the nonlinear control theory and Lyapunov stability theory. The nonlinear controller is designed to ensure the stability and convergence of the proposed synchronization scheme. This technique is applied on the synchronization of two identical fractional-order Chua's circuit systems with memristor. Different examples are studied numerically with different system parameters, different orders, and with five alternative cases where the scaling functions are chosen to be positive/negative and constant/dynamic which covers all possible cases from conventional synchronization to the amplitude modulation cases to validate the proposed concept.

A new method of projective synchronization of unidentical chaotic systems is proposed in this letter. This method is based on the stability criterion of linear systems. The response of two unidentical chaotic systems can synchronize up to any desired scaling factor by a suitable separation of the systems. The new method of projective synchronization is suitable not only for the three-dimensional coupled partially linear systems, but also for higher dimensional even hyperchaotic systems. The simplicity and effectiveness of the proposed method are illustrated by the Lorenz system, the four-dimensional partially linear system, the four-dimensional hyperchaotic Rösser system and Chua's circuit system as four numerical examples.

This article investigates the practical fixed-time synchronization of uncertain coupled neural networks via dual-channel event-triggered control. Contrary to some previous studies, the bipartite synchronization of signed graphs representing cooperative and antagonistic interactions is studied. The communication channel is introduced into deception attacks, which are described by Bernoulli's stochastic variables. Based on the concept of two channels, event-triggered mechanisms are designed for sensor-to-controller and controller-to-actuator channels to reduce communication consumption and controller update consumption as much as possible. Lyapunov and comparison theories are used to derive synchronization criteria and explicit expression of settling time. An example of Chua's circuit system is presented to demonstrate the feasibility of the obtained theoretical results.

Soil salinization is very complex and its evolution is affected by numerous interacting factors produce strong non-linear characteristics. This is the first time fractional order chaos theory has been applied to soil salinization-level classification to decrease uncertainty in salinization assessment, solve fuzzy problems, and analyze the spectrum chaotic features in soil with different levels of salinization. In this study, typical saline soil spectrum data from different human interference areas in Fukang City (Xinjiang) and salt index test data from an indoor chemical analysis laboratory are used as the base information source. First, we explored the correlation between the spectrum reflectance features of soil with different levels of salinization and chaotic dynamic error and chaotic attractor. We discovered that the chaotic status error in the 0.6 order has the greatest change. The 0.6 order chaotic attractors are used to establish the extension matter-element model. The determination equation is built according to the correspondence between section domain and classic domain range to salinization level. Finally, the salt content from the chemical analysis is substituted into the discriminant equation in the extension matter-element model. Analysis found that the accuracy of the discriminant equation is higher. For areas with no human interference, the extension classification can successfully identify nine out of 10 prediction data, which is a 90% identification accuracy rate. For areas with human interference, the extension classification can successfully identify 10 out of 10 prediction data, which is a success rate of 100%. The innovation in this study is the building of a smart classification model that uses a fractional order chaotic system to inversely calculate soil salinization level. This model can accurately classify salinization level and its predictive results can be used to rapidly calculate the temporal and spatial distribution of salinization in arid area/desert soil.

A unidirectional coupling scheme is investigated in double scroll type chaotic oscillators that reveal interesting multiscroll dynamics. Instead of using self-oscillatory systems, in this scheme, double scroll chaos from one oscillator is forced into another similar oscillator in a resting state. This coupling scheme is explored in the Chua oscillator, a modified Chua oscillator and the Lorenz oscillator. We have modified the Chua oscillator by simply changing its piecewise linear function slightly, thereby deriving a new 3-scroll attractor. We have observed 4-scroll, 6-scroll attractors in the driven Chua oscillator and the modified Chua oscillator respectively in an intermittency regime of weaker coupling. We have extended the coupling scheme to the Lorenz system when even more interesting multiscroll dynamics (3-, 4-, 5-, 6-scroll) is observed with decreasing coupling strength. It appears as if a hidden multiscroll structure unfolds with weakening coupling interactions. One after another, additional scrolls appear in the driven Lorenz system when the coupling strength is gradually decreased in the weaker coupling regime. The origin of such multiscroll dynamics is explained using eigenvalue analysis and a bifurcation diagram. A schematic diagram of the multiscroll trajectories is presented to further elucidate the evolution of the scrolls. Experimental evidence is also presented using the Chua circuit and an electronic analog of the Lorenz system.

In this paper, fuzzy impulsive control is used for stabilization of chaotic systems based on the Takagi-Sugeno (T-S) model. The stability issue of the general nonlinear impulsive control system is first investigated via comparison criterion. Then, a novel impulsive control scheme is presented for chaotic systems based on the T-S fuzzy model. Some sufficient conditions are given to stabilize the T-S fuzzy model. Our results are proven to be less conservative theoretically and numerically. Moreover, we have also estimated the stable region of the impulsive interval. Finally, the proposed fuzzy impulsive control scheme is successfully applied to stabilize Rössler's system and Chua's circuit. The numerical simulations demonstrate the effectiveness and advantage of our main results.

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Super Chen chaotic synchronization scheme control which contains both continuous chaotic system with oscillating parameters and discrete chaotic system. If oscillating parameters satisfyingwhen , we proved that two systems can get synchronized without control signal transmitting.