Chaos Generation Research Articles

Parallel Generation of Multi-channel Broadband Chaos by a Long-Cavity FP Laser with Optical Feedback

Parallel Generation of Multi-channel Broadband Chaos by a Long-Cavity FP Laser with Optical Feedback

Enhancing network security with hybrid feedback systems in chaotic optical communication

This paper presents a pioneering approach to bolstering network security and privacy by implementing chaotic optical communication with a hybrid optical feedback system (HOFS). The current baseline methods in network security are often less feasible for hybrid feedback systems, including limited robustness, compromised security, and synchronization challenges. Therefore, this paper proposes a hybrid approach to address these shortcomings by integrating the HOFS into chaotic optical communication systems (HOFS-COCS) to overcome the baseline challenges. This paper aims to improve network security while significantly maintaining efficient communication channels. Moreover, We designed two algorithms, one for chaotic maps generation and another for text encryption and decryption, to improve security in the hybrid feedback system. Our findings demonstrate through rigorous experimentation and analysis that the proposed (HOFS-COCS) method significantly improves network security by enabling reliable chaos generation, synchronization, and secure message transmission in chaotic optical communication systems. This research represents a significant advancement towards enhanced secrecy and synchronization in chaotic optical communication systems, promising a paradigm shift in network security protocols.

Transition to chaos in magnetized rotating Rayleigh-Bénard convection

Transition to chaos and magnetic field generation are investigated in numerical simulations of three-dimensional rotating Rayleigh-Bénard convection. The behavior of the system is explored as a function of the rotation speed, measured by the Taylor number, the thermal buoyancy strength, measured by the Rayleigh number, and the magnetic Prandtl number. In the absence of magnetic field, a detailed exploration of the space of parameters reveals a sequence of Hopf bifurcations leading to quasiperiodicity and chaos. It is shown that rotation can dampen convection for low values of the Rayleigh number, but if buoyancy is strong enough to keep the convection, then rotation facilitates transition to chaos. In the presence of a weak seed magnetic field, convective motions may trigger a nonlinear dynamo that converts kinetic energy into magnetic energy, leading to an exponential increase of the magnetic energy. A nonhysteretic blowout bifurcation is shown to be responsible for the onset of the dynamo regime for a critical magnetic Prandtl number, whose value depends on the rotation rate.

Design of Higher-Dimensional Switching Chaos Generators by Constructing a Closed Hyper-Polyhedron

A novel and unified design approach on higher-dimensional switching chaos generators is derived in this paper. The whole n-dimensional linear space is divided into two parts by a closed hyper-polyhedron. Two higher-dimensional linear systems with the simplest structures as switching chaos generators are designed successfully to generate chaos. State matrix of the first linear system is Hurwitz stable. State matrix of the second linear system is not Hurwitz stable. Chaotic dynamical behaviors take place due to switching two systems. The switching trajectories go through the boundary of the closed hyper-polyhedron endlessly. Moreover, the size of the hyper-polyhedron can determine and control the amplitude of the chaotic signals. Specific numerical examples on four-dimensional, five-dimensional and six-dimensional switching chaos generators are employed, respectively, to illustrate the effectiveness of the novel and advanced approach presented in this paper. The proposed approach can also be applied to designing other switching chaos generators with the higher dimension beyond six.

A family of resonance-based tunable frequency oscillators and application to chaos generation

ABSTRACT We propose a family of second-order resonance-based sinusoidal oscillators with electronically tunable frequencies. Each oscillator is comprised of two amplifiers, surrounded by four impedances which must be a single R , L or C and we show that in this configuration eight resonance-based oscillators are possible. We also show the conditions for each oscillator to oscillate along with the frequency of oscillation and then design a non-autonomous chaotic oscillator based on one of these circuits. Circuit simulations using LTspice and experimental results are presented to verify the theory.

Fractional Order Flux Controlled Meminductive System for Chaos Generation

Fractional Order Flux Controlled Meminductive System for Chaos Generation

Multi-channel broadband optical chaos generation assisted by phase modulation and CFBG feedback

In this paper, we propose a novel and simple multi-channel broadband optical chaos generation scheme based on phase modulation and chirped fiber Bragg grating (CFBG). Firstly, phase modulation is introduced to generate more new frequency components to broaden the spectrum of the phase chaos. Meanwhile, the accumulated dispersion from CFBG distorts the intensity chaos, converts phase chaos to intensity chaos, and weakens the laser relaxation oscillation. This process would lead to energy redistribution in the power spectrum, effectively increasing the chaotic bandwidth. Then, the wavelength detuning between CFBG and the semiconductor laser is introduced to enhance the chaotic bandwidth further. The experiment results show that the 10 dB bandwidths of the five channels are up to 31.0 GHz, 34.3 GHz, 36.3 GHz, 40 GHz, and 40 GHz, respectively. Note that the maximum bandwidth of the PD in our experiment is limited to 40 GHz. In addition, the multi-channel chaotic signals obtained from the experiment system are used to generate multi-channel physical random numbers. After the post-processing operations, the total rate of five parallel high-speed physical random number generation channels is 4.64 Tbit/s (160 GSa/s × 5bit × 1 channel + 160 GSa/s × 6bit × 4 channels). As far as we know, this is the highest record of using external cavity feedback semiconductor lasers to generate random numbers, which has great potential to meet the security requirements of next-generation Tbit/s optical communication systems.

Wideband chaos generation using a VCSEL with intensity modulation optical injection for random number generation

Wideband chaos generation using a VCSEL with intensity modulation optical injection for random number generation

Chaos generation of superconducting quantum bits coupled with LC resonant circuits

The dynamics of chaos have been widely used in nonlinear science, such as neural networks, extreme event statistics, and the biophysics of chaos self-organization. Superconducting qubits are artificial atoms based on the Josephson junction structure of nonlinear superconducting devices, offering high design flexibility and ease of coupling and control. In this paper, the generation of chaos through the coupling between superconducting qubits and LC resonant circuits is investigated. By varying the ratio of Josephson energy to charge energy, the coupling coefficient, and the energy of the external driving field, the generation and control of chaos within the system are numerically analyzed. This study provides theoretical support for parameter selection ensuring the confidentiality and fidelity of quantum information transmission based on the chaotic dynamics of superconducting qubits.

A novel underwater weak signal detection method based on parameter optimized VMD and 3D chaotic system

Based on chaos theory, combined with improved variational mode decomposition, a novel method for underwater weak signal detection and frequency extraction is proposed. The aim of this research is to address the challenge of detecting underwater signals and extracting their frequencies under ultra-low Signal-to-Noise Ratio (SNR). A novel three-dimensional (3D) chaotic system with infinitely shrinking attractors is proposed, which incorporates a cosine function to achieve chaos control and enhancement. The nonlinear characteristics of the system, such as Lyapunov exponent and bifurcation, are analyzed in detail. Then, we design a frequency array and perform scale transformation on the chaotic system to construct a detection model that covering all frequencies. The model can transition from critical chaos to large period or intermittent chaos in the presence of external periodic signals by adjusting the parameters of the cosine function. Considering the relationship between the generation of intermittent chaos and the frequency of target signal, a frequency extraction algorithm based on chaos sparrow search algorithm optimization variational mode decomposition (CSSA-VMD) and Hilbert transform is designed. The algorithm can estimate the real frequency of underwater signals by performing noise reduction and envelope analysis on intermittent chaotic signals. The experimental results demonstrate that the proposed system can detect weak signals in complex marine backgrounds and extract their frequency features, with a detection SNR of -48 dB and a frequency error of less than 0.01%. Importantly, the circuit of the detection system has been implemented, verifying its feasibility for detecting and tracking underwater signals.

Constructing chaotic oscillators with memory components

Memory components, including memristors, meminductors and memcapacitors, have special nonlinear dynamical properties and thus applicable for constructing a compact chaotic circuit in parallel or in series. By selecting the restriction of a memory component, chaos control can also be achieved using a single circuit parameter. In this work, three different types of circuit structures are designed to implement memory components for chaos generation. With the help of a voltage-control or a current-control memristor, within a series or a parallel structure, a memristive chaotic oscillator with partial control is built based on the variable boostable systems. The two constructed structures are equivalent and can be mutually tuned, achieving partial amplitude control as well as offset boosting. By constructing a magnetic-control meminductor or a charge-control memcapacitor, the equivalent parallel circuit is built with a meminductor, a capacitor and a resistor, corresponding to the series circuit with a memcapacitor, an inductor and a resistor. It can be applied to realizing the hypogenetic chaotic jerk system even with conditional symmetry. All the designed circuits are physically realized based on PCB, proving the effectiveness of memory components for chaos generation.

On topological entropy (chaos) realized far from fixed point

In many papers, the concept of chaos is associated with positive topological entropy. The points around which chaos is concentrated are also often examined. In this paper we distinguish places of chaos generation and its realization. Moreover, we will consider the possibility of approximation of continuous function by functions having full entropy point x0 (there is chaos generated by any neighbourhood of it) but simultaneously x0 is not a focal entropy point (chaos is realized at some distance from the considered point).

A Deterministic Chaos-Model-Based Gaussian Noise Generator

The abilities of quantitative description of noise are restricted due to its origin, and only statistical and spectral analysis methods can be applied, while an exact time evolution cannot be defined or predicted. This emphasizes the challenges faced in many applications, including communication systems, where noise can play, on the one hand, a vital role in impacting the signal-to-noise ratio, but possesses, on the other hand, unique properties such as an infinite entropy (infinite information capacity), an exponentially decaying correlation function, and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window, putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criterion on which the main idea of this study is based on is the central limit theorem, which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. This study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.), whose output signals are analyzed according to criteria that encompass the probability density functions of the chaotic signal itself, its envelope, and its phase and statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. Thus, a statistical-characteristic-based algorithm, which includes a series of tests, was developed for a Gaussian-like signal assessment. Following the algorithm, the analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates a Gaussian distribution. This allows for the generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

Broadband electro-optic chaotic system using coupling mutual feedback for intensity and phase chaos generation

An innovative dual-coupled dispersive electro-optic chaotic system utilizing two interlinked nonlinear feedback loops is introduced and demonstrated experimentally. This system efficiently converts phase chaos into intensity chaos while incorporating dispersion, achieved by integrating a broadband chirped fiber Bragg grating (CFBG) into a dual-loop opto-electronic oscillator (OEO) system. Consequently, this leads to the generation of broadband intensity and phase chaos with heightened complexity. Experimental findings indicate that the system achieved up to 24 GHz of 80% bandwidth and 35.5 GHz of 10 dB bandwidth for intensity chaos carriers, and up to 26 GHz of bandwidth with 40.52 GHz of 10 dB bandwidth for phase chaos carriers. The approach features a straightforward structure and mitigates delay characteristics inherently within the system itself. This two-dimensional chaotic source presents potential for secure communications in high-speed Quadrature Amplitude Modulation (QAM) systems.

On the realization of an amplifier‐tuned low/high frequency family of oscillators

SummaryWe propose a family of equal‐R equal‐C dual amplifier oscillators with gain‐tunable start‐up condition and oscillation frequency. In particular, while one of the amplifiers can be used to satisfy the oscillator start‐up condition, the second amplifier can be used to tune the oscillation frequency. In this regard, it is observed that the oscillation frequency can be made very low or very high independent of the RC time constant of the circuit by properly choosing the amplifier gain and the circuit topology. In one possible topology, the oscillation frequency is directly proportional to the tuning amplifier gain, while in a second topology, it is inversely proportional to this gain. Both topologies generate two outputs which also have a gain‐tunable leading or lagging phase shift. Circuit simulations and experimental results are presented to verify the theory in addition to a non‐conventional application in chaos generation.

Broadband chaos generation in a distributed-feedback laser by selecting residual side modes.

Chaotic dynamics with spectral broadening is experimentally obtained by selective excitation of residual side modes in a distributed-feedback (DFB) laser. For the single-mode laser that emits only at the main mode when free-running, feedback to a residual side mode is introduced via a fiber Bragg grating (FBG). The FBG feedback suppresses the main mode, selectively excites the residual side mode, and generates broadband chaotic dynamics. Such a chaos of the residual side mode has a broad electrical bandwidth reaching at least 26 GHz, which corresponds to a significant broadening by over 50% when compared with the main mode. The dynamics are attributed entirely to the one selected mode without invoking multimode interactions. The wavelength is tunable beyond 10 nm by using different FBGs. Through avoiding multimode interactions, this approach of broadband chaos generation is potentially simple to model and thus promising for applications.

Generation of Wideband Chaos With Time-Delay Signature Suppression in Semiconductor Lasers by Asymmetrical Mutual Injection

Generation of Wideband Chaos With Time-Delay Signature Suppression in Semiconductor Lasers by Asymmetrical Mutual Injection

Matrix projective synchronization and mechanical analysis of unified chaotic system

This article explores the mechanical analysis of a unified chaotic system and matrix projective synchronization (MPS). The sufficient conditions to achieve MPS of unified chaotic system have derived. The mechanics of unified chaotic system have been examined in contrast with Kolmogorov system, Euler equation, and Hamiltonian function. The Casimir energy function is also introduced to analyze the system dynamics. The unified chaotic system has been transformed into Kolmogorov type system and decomposed into four types of torques: inertial, internal, dissipation, and external torque. In order to view the mechanics behind the unified chaotic system, different particular cases have been discussed. Five scenarios are examined using combinations of various torques in order to identify the key elements in chaos creation and their physical significance. The bifurcation diagram, Lyapunov exponent and Lyapunov dimension validates the generation of chaos for different particular cases.

Генератор хаотических колебаний

The article analyzes existing schemes of chaos generators. Numerical and simulation modeling is carried out aimed at identifying chaotic dynamics. Based on wellknown concepts, a chaos generator is developed and a simulation model is built. A mathematical description of the generator is given and phase portraits are obtained. Diagrams of chaotic oscillations of the Lorentz model and the Colpitts model are presented. The operation of the Van der Pol generator is considered and the chaotic processes that arise during external harmonic oscillations are shown. Chua's model is presented, its mathematical description is given, and an analysis of oscillations in the deterministic chaos regime is presented.

Broadband Chaos Generation and Synchronization Induced by Integrated Tri-section Laser

Broadband Chaos Generation and Synchronization Induced by Integrated Tri-section Laser