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Because of its excellent performance, the High Dynamic Range (HDR) display becomes more and more popular in many fields. The problem is that most of the display devices available nowadays are still for Low Dynamic Range (LDR) content only. As a result, finding a way to achieve the compatibility between LDR content and HDR content is necessary. In this paper, we provide an improved version of the JPEG-HDR model which allows typical drivers to read and display a tone-mapped image while the HDR information is carried in “sub-band marker.” On the other hand, we can recover the HDR image with the help of inverse tone-mapping operator (iTMO) and “sub-band marker.” It is the backwards-compatible enhancement to HDR. When an application is not designed for HDR imaging, it displays only the tone-mapped image, allowing the user to have access to part of the content. When an application is designed for HDR imaging, we can recover the original HDR image by decoding process.

This paper constructs a new hyperchaotic system based on Lu system by using a state feedback controller. The detailed dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation, and Poincare mapping. Moreover, a novel circuit diagram is designed for verifying the hyperchaotic behaviors and some experimental observations are also given.

This paper proposes a novel nonlinear modulating function approach for generating n-scroll chaotic attractors based on a general jerk circuit. The systematic nonlinear modulating function methodology developed here can arbitrarily design the swings, widths, slopes, breakpoints, equilibrium points, shapes, and even the general phase portraits of the n-scroll chaotic attractors by using the adjustable sawtooth wave, triangular wave, and transconductor wave functions. The dynamic mechanism and chaos generation condition of the general jerk circuit are further investigated by analyzing the system stability. A simple block circuit diagram, including integrator, sawtooth wave and triangular wave generators, buffer, switch linkages, and voltage-current conversion resistors, is designed for the hardware implementations of various 3-12-scroll chaotic attractors via switchings of the switch linkages. This is the first time to experimentally verify a 12-scroll chaotic attractor generated by an analog circuit. In particular, the recursive formulas of system parameters and real physical circuit parameters are rigorously derived for the hardware implementations of the n-scroll chaotic attractors. Moreover, the adjustability of the nonlinear modulating function and the rigorous recursive formulas together provide a theoretical principle for the hardware implementations of various chaotic attractors with a large number of scrolls.

This paper proposes a new approach for constructing higher-dimensional nondegenerate hyperchaotic system with multiple controllers. Here, the so-called higher-dimensional nondegenerate hyperchaotic system means that it can be provided with a maximum number of positive Lyapunov exponents, which has been an open problem for research in recent years. The details of design are given by three steps as follows: (i) Design an [Formula: see text]-dimensional nominal matrix and similarity transformation matrix, and get an asymptotic stable nominal system; (ii) Add a master controller for the nominal matrix and get the controlled system. Then, find suitable control positions such that the controlled system satisfies the average eigenvalue criterion, i.e. the number of average eigenvalues with positive real parts of all Jacobi matrices over a given period of time is equal to ([Formula: see text]), and the maximum value of average eigenvalues with positive real parts is greater than a given threshold [Formula: see text]; (iii) Add nonmaster controllers, and the control positions are fixed and parameters are given in advance. So it can generate nondegenerate hyperchaotic systems with ([Formula: see text]) positive Lyapunov exponents. Finally, two typical examples are given to show the feasibility and effectiveness of the proposed method.

In this paper, a novel approach for constructing one-way hash function based on 8D hyperchaotic map is presented. First, two nominal matrices both with constant and variable parameters are adopted for designing 8D discrete-time hyperchaotic systems, respectively. Then each input plaintext message block is transformed into [Formula: see text] matrix following the order of left to right and top to bottom, which is used as a control matrix for the switch of the nominal matrix elements both with the constant parameters and with the variable parameters. Through this switching control, a new nominal matrix mixed with the constant and variable parameters is obtained for the 8D hyperchaotic map. Finally, the hash function is constructed with the multiple low 8-bit hyperchaotic system iterative outputs after being rounded down, and its secure analysis results are also given, validating the feasibility and reliability of the proposed approach. Compared with the existing schemes, the main feature of the proposed method is that it has a large number of key parameters with avalanche effect, resulting in the difficulty for estimating or predicting key parameters via various attacks.

In this paper, a novel design methodology and its FPGA hardware implementation for a universal chaotic signal generator is proposed via the Verilog HDL fixed-point algorithm and state machine control. According to continuous-time or discrete-time chaotic equations, a Verilog HDL fixed-point algorithm and its corresponding digital system are first designed. In the FPGA hardware platform, each operation step of Verilog HDL fixed-point algorithm is then controlled by a state machine. The generality of this method is that, for any given chaotic equation, it can be decomposed into four basic operation procedures, i.e. nonlinear function calculation, iterative sequence operation, iterative values right shifting and ceiling, and chaotic iterative sequences output, each of which corresponds to only a state via state machine control. Compared with the Verilog HDL floating-point algorithm, the Verilog HDL fixed-point algorithm can save the FPGA hardware resources and improve the operation efficiency. FPGA-based hardware experimental results validate the feasibility and reliability of the proposed approach.

In this paper, a novel approach is developed for multi-images encryption and decryption by using single discrete time chaotic system and anti-control methodology. The field programmable gate array (FPGA) embedded implementations are demonstrated, and the corresponding NIST safety performance test results are also given.

Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.

This paper introduces a novel approach for generating continuous-time autonomous hyperchaotic systems with multiple positive Lyapunov exponents. In detail, this paper develops two general design principles for constructing various hyperchaotic systems with desired numbers of positive Lyapunov exponents. Two typical examples are then given to verify the proposed design principle. In particular, the developed method can design hyperchaotic systems with any multiple positive Lyapunove exponents by following a unified procedure compared with the traditional trial-and-error approach.

This paper proposes a chaotic secure video remote communication scheme that can perform on real WAN networks, and implements it on a smartphone hardware platform. First, a joint encryption and compression scheme is designed by embedding a chaotic encryption scheme into the MJPG-Streamer source codes. Then, multiuser smartphone communications between the sender and the receiver are implemented via WAN remote transmission. Finally, the transmitted video data are received with the given IP address and port in an Android smartphone. It should be noted that, this is the first time that chaotic video encryption schemes are implemented on such a hardware platform. The experimental results demonstrate that the technical challenges on hardware implementation of secure video communication are successfully solved, reaching a balance amongst sufficient security level, real-time processing of massive video data, and utilization of available resources in the hardware environment. The proposed scheme can serve as a good application example of chaotic secure communications for smartphone and other mobile facilities in the future.

This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors' knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.

In this paper, a novel approach for digital image encryption and decryption via embedded FPGA Ethernet transmission is proposed. Taking multi-wing butterfly chaotic attractor as an example, based on Euler algorithm and variable ratio expansion transformation, by programming C language under the Linux operating system, the continuous time chaotic system is converted to the discrete chaotic system and the digital chaotic sequence is generated as image encryption and decryption on the embedded FPGA-based platform. According to the principle of driving-response synchronization, a scheme for chaotic secure communication of a 512×512BMP static color image is implemented via Ethernet transmission on the embedded FPGA platform with XUP Virtex-II Pro chip. Moreover, the system design, software simulation and hardware implementation results are also given.

Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method of designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystem, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general., Comment: 17 pages, 11 figures

This paper presents a novel four-dimensional (4D) smooth autonomous system. The prosposed system is special since it has only one equilibrium, but it can generate a four-wing chaotic or hyperchaotic attractor. By applying either analytical or numerical methods, some basic properties of the 4D system, such as phase diagrams, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. And the improved form is proposed by introducing changeable sine periodic signal into one of the state variable of the 4D system. It is confirmed that the improved 4D system always holds two invariable positive Lyapunov exponents when the external sine periodic signal works, and still displays four-wing hyperchaotic behaviour.

In this paper, based on LaSalle's invariance principle and linear matrix inequality (LMI), two novel synchronization criteria for the unified chaotic systems with known or unknown parameters are investigated. In comparison with previous methods, the presented controller contains single state feedback. To our knowledge, the above control scheme is the simplest for synchronizing the unified chaotic system. The theoretical analysis and numerical simulation results are also given, conforming the effectiveness of the proposed scheme.

The complete synchronization and anti-synchronization(C-A synchronization) can be achieved when chaotic system has some degree of symmetry. In this paper, C-A synchronization is improved based on the linear separation method to achieve the C-A projective synchronization, that is, the drive and response vectors synchronize up to the scaling factor in the Lorenz system. Furthermore, the controller obtained by the improved C-A synchronization is modified by a large quantity of trial-and-error computer simulations to generate a special multi-wing chaotic attractor. By the theoretical analysis and numerical simulations, some basic dynamical properties of the controlled Lorenz system are investigated. Research results show that this system has complex and interesting chaotic and hyperchaotic dynamics.

There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation. Although saddle foci of index 2 have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper. A novel approach for constructing chaotic systems is investigated by applying the switching control strategy and yielding a heteroclinic loop which connects two saddle foci of index 1. A basic 3-D linear system with an arbitrary normal direction of the eigenplane, possessing a saddle focus of index 1 whose corresponding eigenvalues satisfy the Shil'nikov inequality, is first introduced. Then a heteroclinic loop connecting two saddle foci of index 1 will be formed by applying the switching control strategy to the basic 3-D linear system. The heteroclinic loop consists of an unstable manifold, a stable manifold, and a heteroclinic point. Under the necessary conditions for forming the heteroclinic loop, the intended two-segmented piecewise linear system which exhibits the chaotic behavior in the sense of the Smale horseshoe can be finally constructed. An illustrative example is given, confirming the effectiveness of the proposed method.

This paper constructs a 4-D hyper chaotic Chua system via state feedback control, based on 3-D Chua system with both piecewise-linear and smooth cubic nonlinearity. Dynamical behaviors of this hyper chaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of equations. Numerical results show this system can generate hyper chaotic multi-scroll attractors.

In this paper, a novel approach for digital image chaotic communication via FPGA embedded Ethernet transmission is proposed. Based on Euler algorithm and variable ratio expansion transformation, by C language programming under the Linux operating system, the continuous time 8-scroll Chua system is converted to the discrete sequence used to encrypt and decrypt image on the FPGA-based platform. According to the principle of driving-response synchronization, a scheme for chaotic communication of a 512×512BMP static color image is implemented via embedded Ethernet transmission on the FPGA-based platform with XUP Virtex-II Pro chip. Moreover, the system design, software simulation and hardware implementation results are also given.

The wide application of Binary segmentation for grayscale images could be found in computer vision and pattern recognition, especially for the purpose of object identification and recognition with industry and military images. This paper proposes a noise robust binary segmentation approach which incorporates Ant Colony System (ACS) with the modified Fuzzy C-Means (FCM) clustering algorithm. The ACS first survey the whole image, adding an additional pheromone dimension other than grayscale on each pixel. The modified FCM then deems every pixel a 2-dimensional vector and classifies all image pixels into two categories. Experiments have demonstrated better segmentation results and the advantage of robustness against noise using this method.

Though FCM has long been widely used in image segmentation, it yet faces several challenges. Traditional FCM needs a laborious process to decide cluster center number by repetitive tests. Moreover, random initialization of cluster centers can let the algorithm easily fall onto local minimum, causing the segmentation results to be suboptimal. Traditional FCM is also sensitive to noise due to the reason that the pixel partitioning process goes completely in the feature space, ignoring some necessary spatial information. In this paper we introduce a modified FCM algorithm for color image segmentation. The proposed algorithm adopts an adaptive and robust initialization method which automatically decides initial cluster center values and center number according to the input image. In addition, by deciding the window size of pixel neighbor and the weights of neighbor memberships according to local color variance, the proposed approach adaptively incorporates spatial information to the clustering process and increases the algorithm robustness to noise pixels and drastic color variance. Experimental results have shown the superiority of modified FCM over traditional FCM algorithm.

Ant Colony Optimization (ACO) is a newly proposed intelligent algorithm for solving discrete optimization problems such as the Travelling Salesman Problem (TSP). In this paper we introduce a novel ACO-based clustering algorithm and exploit its application in image segmentation. Unlike traditional ACO which is mainly based on probabilistic and hard path choosing, the proposed method utilizes a soft and fuzzy scheme. In detail, every pixel in the image is viewed as an ant and the calculation of membership function is based on heuristic and pheromone information on each cluster center. In addition, memberships are modified to include spatial information which can further improve the algorithm performance for image segmentation. Experiments are taken to examine the performance of ACO-based fuzzy clustering algorithm and segmentation results indicate that the proposed approach has the potential of becoming an established clustering method for image segmentation.

In this paper, a new fourth-order chaotic circuit is proposed. The circuit includes two linear inductors, two linear capacitances, a linear negative resistance, and two non-linear elements, thus, to construct a chaotic circuit with structure. Theoretical analysis, numerical simulation and circuit implementation has confirmed the effectiveness of this approach.

This paper initiates a novel approach for generating multi-wing butterfly chaotic attractors from the piecewise-linear Chen system by constructing a duality-symmetric multi-piecewise linear function. It should be pointed out that this proposed method is different from the traditional techniques. Furthermore, its dynamical behaviors are then further investigated and the numerical simulations are also given.

In this paper, a multiple piecewise-linear function is constructed for generating multi-scroll chaotic attractors from the fifth-order Chua system. This approach has been verified both in theoretical analysis and computer simulations.

This paper proposes a novel multiscroll chaotic system, which is different from Chua's circuit and all its variants in most aspects of the algebraic form, circuit design, and geometrical structure of the attractor. In particular, the multiscroll attractor of this new system is more complex than that of the generalized Chua's circuit when they both have the same number of scrolls. The dynamical behaviors of the new system are then analyzed, including the bifurcation diagram and the Lyapunov exponent spectra. Moreover, a module-based circuit diagram is designed for realizing various multiscroll attractors. Finally, experimental circuits are implemented with physical observations reported.

Based on the sawtooth wave function, this paper initiates an approach for generating novel multi-wing butterfly chaotic attractors from the generalized first and second types of modified Lorenz systems. Our theoretical analysis shows that every index-2 saddle-focus equilibrium corresponds to a unique wing in the butterfly attractors. Compared with the traditional ring-shaped multiscroll Lorenz chaotic attractors, the proposed multi-wing butterfly chaotic attractors are much easier to be constructed and implemented by analog circuits. Furthermore, a module-based unified circuit diagram is designed for realizing various multi-wing attractors.

We demonstrate the design and experimental implementation of an electro-optic control system that is used to detect the arrival of packets at the optical switch input, process the headers of the packets, and control switching according to the header content for both fixed and variable length packets. We also demonstrate the flexibility of the electro-optic crosspoint switch for implementation in a photonic packet switching (PPS) network. Furthermore, contention resolution is demonstrated in the electro-optic crosspoint switch by detecting packets at the input ports and controlling the switch operation accordingly. By incorporating this control system into the crosspoint switch it is possible to route contending packets to a re-circulating fiber delay line and control the switch output in a flexible manner for any type of traffic depending on the applied switching algorithm. The experiments are carried out with 155 Mbit/s headers and 10 Gbit/s payloads transmitted on a single wavelength with a guard time of 12.8 ns between header and payload. PPS with bit error rate (BER) less than 10-9 is demonstrated. Error free contention resolution is shown with the main signal degradation being from the switch cell attenuation and amplifier ASE that can be alleviated by eliminating fiber-to-fiber transmission loss in the crosspoint.

A systematic methodology for generating multi-folded torus chaotic attractors from a simple three-dimensional piecewise-linear system is presented in this paper. Theoretical analysis shows that multi-folded torus chaotic attractors can be created via alternative switching between two piecewise-linear systems. A novel circuit diagram is designed for physically creating multi-folded torus chaotic attractors. This is the first time in the literature to experimentally verify a maximum 9-folded torus chaotic attractor that is generated by an analog circuit.

A systematic circuit design approach is proposed for experimental verification of hyperchaotic 2, 3, 4-scroll attractors from a generalized Matsumoto-Chua-Kobayashi (MCK) circuit. The recursive formulas for system parameters are rigorously derived for improving the hardware implementation.

This paper introduces a novel circuit design for experimental verification of 3D hysteresis multi-scroll chaotic attractors. A block circuit diagram is shown for realizing 1D 5/spl sim/11-scroll, 2D 3/spl times/5/spl sim/11-grid scroll, and 3D 3/spl times/3/spl times/5/spl sim/11-grid scroll chaotic attractors by operating the switches. Moreover, this design provides a theoretical principle for hardware implementation of chaotic attractors in multi-directions with a large number of scrolls.

The paper proposes a novel nonlinear modulating function approach for generating N-scroll chaotic attractors based on a general jerk circuit. The systematic nonlinear modulating function methodology developed can arbitrarily design the swings, widths, slopes, breakpoints, equilibrium points, and shapes of the N-scroll chaotic attractors; via the adjustable sawtooth wave, triangular wave, and transconductor wave functions. A block circuit diagram is designed for hardware implementation of various 3- to 12-scroll attractors via switchings of the switch linkages. This is the first time that a 12-scroll chaotic attractor, generated by an analog circuit under laboratory conditions, has been verified experimentally.

This paper investigates n-dimensional discrete-time systems with modulus of triangular wave functions. First, a proof is given to the existence of chaos in the sense of Li–Yorke. Then, taking the three-dimensional case as a typical example, a circuit is designed under the condition of a limited region, with experimental results demonstrated.

In this paper, discrete-time chaotic systems under single state variable feedback control are studied, and drive-response synchronization is investigated. To that end, ARM platform-based digital color image encryption and decryption using a chaotic stream cipher is designed and implemented, with experimental results demonstrated.

In this paper, we propose a ring-scroll Chua system by introducing a generalized ring transformation. Some basic dynamical properties of this generalized ring transformation are discussed. The parameter regions and the periodic orbits, which are embedded in Chua chaotic attractor mapping to those in ring-scroll Chua chaotic attractor, are investigated, too. Moreover, the topological horseshoe of this system is investigated. Finally, the ring-scroll Chua chaotic attractor is physically implemented by using digital signal processors.

This paper further investigates a novel method, namely the mirror and double-mirror symmetry conversion both in z direction and in y direction, for generating complex grid multiwing chaotic attractors from a three-dimensional quadratic chaotic system. First, by designing a switching controller with even-symmetry multisegment quadratic function to extend the number of saddle-focus equilibrium points with index 2 in x direction, multiwing chaotic attractors are obtained. Based on this approach, then, different from the methods proposed in the previous literature, by the mirror and double-mirror symmetry conversion with respect to x-axis and y-axis respectively, various intended grid n × m-wing chaotic systems can be obtained. The principle and method for generating grid multiwing are also given. Numerical simulations and circuit realizations have demonstrated the feasibility and effectiveness of the proposed approaches.

In this paper, a novel approach is proposed for generating fractional-order multiwing chaotic attractors. Based on a fractional-order linear differential system, by introducing the nonlinear state feedback controller equipped with an even symmetric multisegment quadratic function, various fractional-order multiwing chaotic attractors can be generated. An improved module-based circuit is also designed for verifying the effectiveness of the proposed method.

In this paper we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (PMSM). The necessary condition for the existence of chaos in the fractional-order PMSM is deduced. And an adaptive-feedback controller is developed based on the stability theory for fractional systems. The presented control scheme, which contains only one single state variable, is simple and flexible, and it is suitable both for design and for implementation in practice. Simulation is carried out to verify that the obtained scheme is efficient and robust against external interference for controlling the fractional-order PMSM system.

This paper reports an autonomous-system-based approach for creating compound chaotic attractors from a class of generalized Lorenz systems via switching control. A state variable scale transformation is proposed for these systems to ensure that all attractors have comparable sizes. Coordinate transformation in the z-axis direction is also used, so that every pair of adjacent chaotic attractors have a common connected domain in the same phase space. Then, by switching control, the intended compound chaotic attractors can be generated. A circuit for a compound Lorenz–Chen–Lü chaotic attractor is designed and implemented for demonstration, which verifies the effectiveness of the proposed simulation-based technique. The aim of this report is to demonstrate the possibility of accomplishing such a very challenging task, leaving the extremely difficult underlying theory to future studies.

In this paper, a 4D hyperchaotic Chua system both with piecewise-linear nonlinearity and with smooth and piecewise smooth cubic nonlinearity is introduced, based on state feedback control. Dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of state equations. Theoretical analysis and numerical results show that this system can generate multiscroll hyperchaotic attractors. In addition, a circuit is designed for 4D hyperchaotic Chua system such that the double-scroll and 3-scroll hyperchaotic attractors can be physically obtained, demonstrating the effectiveness of the proposed simulation-based techniques.

This paper proposes a systematic methodology for creating multifolded torus chaotic attractors from a simple three-dimensional piecewise-linear system. Theoretical analysis shows that the multifolded torus chaotic attractors can be generated via alternative switchings between two basic linear systems. The theoretical design principle and the underlying dynamic mechanism are then further investigated by analyzing the emerging bifurcation and the stable and unstable subspaces of the two basic linear systems. A novel block circuit diagram is also designed for hardware implementation of 3-, 5-, 7-, 9-folded torus chaotic attractors via switching the corresponding switches. This is the first time a 9-folded torus chaotic attractor generated by an analog circuit has been verified experimentally. Furthermore, some recursive formulas of system parameters are rigorously derived, which is useful for improving hardware implementation.

This paper proposes a general multiscroll Lorenz system family by introducing a novel parameterized nth-order polynomial transformation. Some basic dynamical behaviors of this general multiscroll Lorenz system family are then investigated, including bifurcations, maximum Lyapunov exponents, and parameters regions. Furthermore, the general multiscroll Lorenz attractors are physically verified by using digital signal processors.