Amr Elsonbaty

Circuit realization, bifurcations, chaos and hyperchaos in a new 4D system

Abstract This paper is devoted to introduce a new four-dimensional hyperchaotic system. Existence and uniqueness of the solution of the proposed system are proved. Continuous dependence on initial conditions of the system’s solution and some stability conditions of system’s equilibrium points are studied. The existence of pitchfork bifurcation is demonstrated by using the center manifold theorem and the local bifurcation theory. The Hopf bifurcation is examined in double parameters bifurcation diagrams along with degenerate types of Hopf bifurcations. The rich dynamical behaviors of the system are explored, then circuit implementation of the system is proposed. Numerical simulations are carried out to verify theoretical analysis.

Simultaneous Suppression of Time-Delay Signature in Intensity and Phase of Dual-Channel Chaos Communication

In this paper, we propose a novel dual-channel optical chaos system with a time-delay (TD) feature simultaneously suppressed in all observables, i.e., in both intensity and phase. A hybrid optical and electro-optic feedback for a single vertical-cavity surface-emitting laser (VCSEL) is verified to induce simultaneous TD suppression for the polarization-resolved components of the chaotic output. A comprehensive mathematical model is developed to incorporate the optical and electro-optic time delays into the rate equations of the VCSEL. The suppression of TD signature is then examined by means of autocorrelation function and delayed mutual information. The results show that the output chaotic signal has the TD feature well eliminated in both the intensity and phase over certain regions of parameter space identified using the peak signal to mean ratio technique. The independent evolution of the two orthogonal VCSEL modes renders the polarization-resolved output modes appropriate for the enhanced dual-channel chaos applications. To the best of our knowledge, this is the first time that a dual-channel chaos communication system is reported with simultaneous suppression of the TD feature in all the transmitted observables.

Numerical analysis of ultrafast physical random number generator using dual-channel optical chaos

Abstract. Fast physical random number generators (PRNGs) are essential elements in the development of many modern applications. We numerically demonstrate an extraction scheme to establish an ultrafast PRNG using dual-channel optical-chaos source. Simultaneous suppression of time-delay signature in all observables of the output is verified using autocorrelation-function method. The proposed technique compares the level of the chaotic signal at time t with M levels of its delayed version. The comparators [1-bit analog-to-digital converters (ADCs)] are triggered using a clock subject to an incremental delay. All the delays of the chaotic signal before the ADCs and the relative delays of the clock are mutually incommensurable. The outputs of the ADCs are then combined using parity-check logic to produce physically true random numbers. The randomness quality of the generated random bits is evaluated by the statistical tests of National Institute of Standards and Technology Special Publication 800-22. The results verify that all tests are passed from M=1 to M=39 at sampling rate up to 34.5 GHz, which indicates that the maximum generation rate of random bits is 2.691  Tb/s without employing any preprocessing techniques. This rate, to the best of our knowledge, is higher than any previously reported PRNG.

A new technique for ultrafast physical random number generation using optical chaos

In this paper, we numerically demonstrate a new extraction scheme for generating ultra-fast physically random sequence of bits. For this purpose, we utilize a dual-channel optical chaos source with suppressed time delayed (TD) signature in both the intensity and the phase of its two channels. The proposed technique uses M 1-bit analog-to-digital converters (ADCs) to compare the level of the chaotic intensity signal at time t with its levels after incommensurable delay-interval Tm, where m = {1,2, … , M}. The binary output of each 1-bit ADC is then sampled by a positive-edge-triggered D flip flop. The clock sequence applied to the flip-flops is relatively delayed such that the rising edge of the clock triggering the m flip-flop precedes the rising edge of the clock of a subsequent m+1 flip-flop by a fixed period. The outputs of all flip flops are then combined by means of a parity-check logic. Numerical simulations are carried out using values of parameters at which TD signature is suppressed for chosen values of setup parameters. The 15 statistical tests in Special Publication 800-22 from NIST are applied to the generated random bits in order to examine the randomness quality of these bits for different values of M. The results show that all tests are passed from M = 1 to M = 39 at sampling rate up to 34.5 GHz which indicates that the maximum generation rate of random bits is 2.691 Tb/sec using a chaotic source of single VCSEL and without employing any pre-processing techniques.

Suppressed time delay signature in chaotic nanolasers with hybrid feedback

In this paper, we investigate the presence of time delay (TD) signature in the chaotic emission of semiconductor metalclad nanolasers subject to different types of optical feedbacks (OFs). We first examine the TD signatures in the cases when all-optical feedback via either conventional mirror, phase conjugate mirror, or grating mirror is employed. Second, we propose a mixed all-optical / electrooptic feedback scheme for concurrent suppression of TD feature in chaotic output emission. The mathematical model for proposed scheme is presented to integrate both the optical and electrooptic time delays. The concealment of TD signature is then investigated by means of the autocorrelation function. The results reveal that the chaotic output signal in each case has well eliminated TD signature at particular operational regions within which the system is more appropriate for applications related to secure communications and ultra-fast physical random number generators.

Further analytical bifurcation analysis and applications of coupled logistic maps

Abstract In this work, we extend further the analytical study of complex dynamics exist in two coupled logistic maps. New results about the occurrence of various types of bifurcation in the system, including flip bifurcation, pitchfork bifurcation and Neimark–Sacker bifurcation are presented. To the best of authors’ knowledge, the presence of chaotic dynamics in system’s behavior has been investigated and proved analytically via Marotto’s approach for first time. Numerical simulations are carried out in order to verify theoretical results. Furthermore, chaos based encryption algorithm for images is presented as an application for the coupled logistic maps. Different scenarios of attacks are considered to demonstrate its immunity and effectiveness against the possible attacks. Finally, a circuit realization for the coupled logistic maps is proposed and utilized in a suggested real time text encryption system.

Time delay signature of chaotic nanolasers and its concealment

In this paper, we investigate the presence of time delay (TD) signature in chaotic intensity outputs of nanolasers subject to different optical feedbacks (OFs). Simulation results reveal the occurrence of obvious TD feature for the cases where conventional, phase conjugate and grating mirror feedbacks are employed. So, a proposed scheme for generating optical chaos with concealed TD signature is proposed to overcome the drawbacks of previously mentioned OFs and render the system more appropriate for applications of secure communications and fast physical random number generators.

Hyperchaotic Fractional-Order Systems and Their Applications

Research about fractional-order hyperchaotic systems gains a lot of interest from both theoretical and applied point of view. Some fractional-order hyperchaotic systems have been investigated, such as the fractional-order hyperchaotic Rossler system and the fractional-order hyperchaotic Chen system. Recent publications in this area include nonlinear circuits, secure communication, laser applications, spread spectrum communication, communication in star coupled network, video encryption communication, color image encryption algorithm, and applications of different types of synchronization. We are pleased to announce the publication of this special issue focusing on novel topics in hyperchaotic fractional-order systems and their applications. The main objective of this special issue is to provide an opportunity to study the new developments related to novel chaotic systems, synchronization schemes, bifurcations, and control in hyperchaotic fractional-order systems along with their applications. Among the articles that were submitted for review, our editorial team has selected seven articles for publication. These articles cover the topics of adaptive fuzzy synchronization, image encryption algorithm, dynamical analysis of a novel hyperchaotic system, eigenvalue problems, BAM neural networks with distributed delays and impulses, complex synchronization scheme between integer-order and fractional-order chaotic systems with different dimensions, and fractional-order FPGA implementation. We are confident that this special issue advances the understanding and research of hyperchaotic fractional-order systems and their applications.

Chaotic DPSK-MPPM modulation technique for a physically secure and highly robust optical communication system

In this paper, we present a novel chaotic hybrid DPSK-MPPM modulation technique which is ultimately secure, spectrally efficient, and highly detection-sensitive. The position and phase information are perturbed by two variables of 2D chaotic map. The BER performance of the proposed scheme is then evaluated numerically and compared with that of the CPPM.