Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

Function Projective Synchronization of Two Identical New Hyperchaotic Systems

A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.

Function projective lag synchronization of fractional-order chaotic systems

Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point; a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle＇s invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization （FPS） in drive–response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.

Automatically Eye Detection with Different Gray Intensity Image Conditions

One of the methods for biometric identification is facial features detection, and eye is an important facial feature in the face. In the recent years, automatically detecting eye with different image conditions is attended. This paper proposes a method which can automatically detect eye in extensive range of images with different conditions. In the proposed method, first an image is enhanced by morphological operations then region of face is detected by hybrid projection function. To identify window of eye, vertical edge dominance map is used. The authors＇ method uses elliptical mask on eye image to detect center of pupil. The mask scans eye image to find minimum gray level because pupil is darkest part in eye image compared with 3 well-known methods. The accuracy of 99.53% on this This method has implemented on JAFFE face database and database confirms efficiency of the proposed method.

A function cascade synchronization method with unknown parameters and applications

This paper investigates the function cascade synchronization of chaos system. Combining cascade synchronization scheme, parametric adaptive control and projective synchronization scheme, it proposes a new function cascade synchronization scheme to address a generalized-type synchronization problem of three famous chaotic systems： the Lorenz system, Liu system and RSssler system, the states of two identical chaotic systems with unknown parameters can be asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.

Function Projective Synchronization of Discrete-Time Chaotic and Hyperchaotic Systems Using Backstepping Method

In this paper, a function projective synchronization scheme is developed to investigate the function projective synchronization between the discrete-time driven chaotic system and the discrete-time response chaotic system. With the aid of symbolic-numeric computation, we use the scheme to study the function projective synchronization between 2D Lorenz discrete-time system and Hdnon discrete-time system, as well as that between 3D discrete-time hyperchaotic system and Henon-like map via three scalar controllers, respectively. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme.

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization （FPS） of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme.

Function projective synchronization in partially linear drive-response chaotic systems

This paper gives the definition of function projective synchronization with less conservative demand for a scaling function, and investigates the function projective synchronization in partially linear drive-response chaotic systems. Based on the Lyapunov stability theory, it has been shown that the function projective synchronization with desired scaling function can be realized by simple control law. Moreover it does not need scaling function to be differentiable, bounded and non-vanished. The numerical simulations are provided to verify the theoretical result.

A general method for modified function projective synchronization

This paper investigates the modified function projective synchronization,which means that the drive system and the response system are synchronized up to a desired scale matrix of function. By the active control scheme,a general method for modified function projective synchronization is proposed. Numerical simulations on chaotic Rssler system and hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme.

Function Projective Synchronization between Two Discrete-Time Hyperchaotic Systems Using Backstepping Method

We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the backstepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

The Cartography of Focus and Interrogative Projections inǸjò`-Kóo

Researches on cartography have made universal predictions on the hierarchies of functional projections in language.Based on this assumption,the structural maps established by Rizzi(1997,2001b)for the left-peripheral elements suggest very strongly that Interrogative dominates Focus.Nevertheless,a straight-jacket adoption of this proposed hierarchical order to account for these left-peripheral projections inǸjò`-Kóo would be counterintuitive.Therefore,leaning on empirical and theoretical evidence,the paper calls to question the universality of the cartographers’claim,and argues that the opposite of the view is true ofǸjò`-Kóo.The paper adopts fieldwork method for data elicitation and descriptive approach as well as minimalist program for analysis of data.Data used in this study were elicited from purposively selected native speakers based on language proficiency.Data were acquired with syntactic checklist and structured interviews,and were subjected to interlinear and qualitative analysis.

Hybrid Function Projective Synchronization of Chaotic Systems with Uncertain Time-varying Parameters via Fourier Series Expansion

In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.

Bounded Projections and Duality on Spaces of Holomorphic Functions in the Unit Ball of (?)~n

In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).

Counting Multiplicities in a Hypersurface over Number Fields

We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.

Reliable iris localization using integral projection function and 2D-shape properties

Iris recognition technology recognizes a human based on his/her iris pattern. However, the accuracy of the iris recognition technology depends on accurate iris localization. Localizing a pupil region in the presence of other low-intensity regions, such as hairs, eyebrows, and eyelashes, is a challenging task. This study proposes an iris localization technique that includes a localizing pupillary boundary in a sub-image by using an integral projection function and two-dimensional shape properties （e.g., area, geometry, and circularity）. The limbic boundary is localized using gradients and an error distance transform, and the boundary is regularized with active contours. Experimental results obtained from public databases show the superiority of the Drooosed techniaue over contemporary methods.

A generalized approach for implicit time integration of piecewise linear/nonlinear systems

A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed.The piecewise linear characteristic has been well‐discussed in previous studies,in which the original problem has been transformed into linear complementarity problems(LCPs)and then solved via the Lemke algorithm for each time step.The proposed scheme,instead,uses the projection function to describe the discontinuity in the dynamics equations,and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration.Compared with the LCP‐based scheme,the new scheme offers a more general choice by allowing other nonlinearities in the governing equations.To assess its performances,several illustrative examples are solved.The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems,but also exhibits substantial efficiency advantages over the LCP‐based scheme when applied to piecewise linear systems.