Stability and Intermittency in Large-Scale Coupled Oscillator Models for Perceptual Segmentation

A highly efficient, low-order model for vortex-induced vibration of flexible cables at low Reynolds number has been developed. A coupled map lattice (CML) wake model, based on circle maps, is combined with a cable model (linear wave equation). With this model, both the self-excited response of the cable oscillation in the crossflow direction and the resulting wake structures are examined at Re = 100. This represents an improvement over earlier CML models capable of only modelling wakes behind externally forced cables. For comparison, spectral-element based numerical simulations, in addition to experiments on a freely vibrating cable flow, were conducted. The freely vibrating CML model predicted lace-like structures consistent with these numerical simulations and experimental results. Little difference was noted between the vortex shedding wake patterns determined for forced cables (from previous CML models) and freely vibrating cables. The freely vibrating CML matched experimental data for maximum cable amplitude reasonably well over a range of mass-damping parameter employed in offshore structural applications.

The coupled map lattices (CML) is a spatiotemporal chaotic system with complex dynamic behavior. In this paper, we propose a spatiotemporal chaotic system with a novel pseudo-random coupling method based on elementary cellular automata (ECA), and introduce different perturbations into lattices in each iteration according to ECA. We investigate the spatiotemporal dynamic properties and chaotic behaviors of the proposed system such as bifurcation diagrams, Kolmogorov Sinai entropy, and uniformity. Moreover, the randomness of sequences generated by the proposed system and the correlation between any two lattices are discussed. Theory analyses and simulations indicate that the new system has better performance in complexity, ergodic and unpredictability than other CML systems such as adjacent CML and nonlinear CML based on fractional order logistic equation, etc. Furthermore, the correlation coefficient between any two lattices in the proposed system is significantly lower than other systems, and another advantage of the proposed system is utilizing the output of ECA to perturb the chaotic system which can effectively alleviate the dynamical degradation in digital system. The excellent performance of the proposed system demonstrates that it has great potential for crypto-system.

Chaos has been widely combined with cryptography in the field of information security, especially, a considerable amount of studies of generating pseudo-random numbers based on chaotic systems have been proposed in recent decades. However, many of them are easy to be attacked via utilizing the nonlinear prediction method based on phase space reconstruction and other analysis. Furthermore, under the finite precision environment of computer simulation, there does not exist a random sequence which is truly non-periodic. Unfortunately, few researches had made a related analysis on the above two discussions. This paper is devoted to designing a pseudo-random number generator based on coupled map lattice with time-varying delay, analyzing the random properties of the generated pseudo-random numbers and discussing the dynamical degradation of the system under finite precision of computer simulation. The proposed scheme merely depends on the determining equation; thus, the algorithm itself is not complex, which does not impose high demand on computer hardware and its efficiency is excellent. In order to meet the requirements of using the proposed pseudo-random number generator in cryptography and other practical engineering applications, the proposed pseudo-random number generator is subjected to statistical tests utilizing the well-known test suites, such as NIST SP800-22 and TestU01. Moreover, other related properties, such as permutation entropy, invariant distribution, degradation of dynamical characteristics and parameter test, are also investigated. All results illustrate that the new pseudo-random number generator can generate a high percentage of available pseudo-random numbers for scientific computer simulation and practical applications in the field of information security.

Coupled map lattices (CMLs) offer a new framework for modelling visual information processes. The framework involves computing with non-stationary patterns of synchronized activity. In this framework structural features of the visual field emerge through the lateral interaction of locally coupled non-linear maps. Invariant representations develop independent of top-down, or re-entrant, feedback. These representations distort certain features of the pattern, giving rise to visual field illusions. Boundary contours, among others, are emphasized, which suggests that special cases of boundary contour problem could be solved by the system. Simulation studies were performed to test the hypothesis that the system represents visual patterns in a solid/outline invariant manner. A standard back-propagation neural network trained with a CML-filtered set of solid images and tested with CML-filtered outline versions of the same set of images (or vice versa) showed perfect generalization. Generalization failed to occur for unfiltered or contour-filtered images. The CML representations, therefore, were concluded to be solid/outline invariant.

The topic of utilizing coupled map lattice to investigate complex spatiotemporal dynamics has attracted a lot of interest. For exploring the spatiotemporal complexity of a predator‐prey system with migration and diffusion, a new three‐chain coupled map lattice model is developed in this research. Based on Turing instability analysis, pattern formation conditions for the predator‐prey system are derived. Via numerical simulation, rich Turing patterns are found with subtle self‐organized structures under diffusion‐driven and migration‐driven mechanisms. With the variation of migration rates, the predator‐prey system exhibits a gradual dynamical transition from diffusion‐driven patterns to migration‐driven patterns. Moreover, new results, the self‐organization of non‐Turing patterns, are also revealed. We find that even in the cases where the nonspatial predator‐prey system reaches collapse, the migration can still drive pattern self‐organization. These non‐Turing patterns suggest many new possible ways for the coexistence of predator and prey in space, under the effects of migration and diffusion.

This paper broadens the research on planar Mandelbrot set to the spatial case by investigating the Mandelbrot set generated in coupled map lattice (CML M-set for short). The visualization and symmetry property of the 3D slice of CML M-set are investigated. Furthermore, a proper controller is designed for the 3D slice of CML M-set to achieve its symmetry change, position change and size change. Numerical simulations are included to verify the effectiveness of the control method.

In this study, the modelling and simulation of chaotic Rossler system has been carried out by using an intelligent system based on neuro-fuzzy modelling technique. Furthermore, the MATLAB simulation of chaotic Rossler system has been carried out for comparison with proposed technique. Structure of the Adaptive Neuro-Fuzzy Inference System (ANFIS) is improved and trained in MATLAB toolbox. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the ANFIS network. Numerical simulations are used in this study. We have used four various data sets for testing the simulation speed of ANFIS and MATLAB. Obtained Results show that the proposed modelling technique has much higher speed and accuracy in comparison with MATLAB simulation. The neuro-fuzzy modelling technique can be simply used in software tools for designing and simulation of the chaotic Rossler system and the other chaotic systems.

Tracking control for the output using an observer-based H ∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations.

Adaptive control of spatiotemporal chaos in coupled map lattices

Audio encryption has gained popularity in a variety of fields including education, banking over the phone, military, and private audio conferences. Data encryption algorithms are necessary for processing and sending sensitive information in the context of secure speech conversations. In recent years, the importance of security in any communications system has increased. To transfer data securely, a variety of methods have been used. Chaotic system-based encryption is one of the most significant encryption methods used in the field of security. Chaos-based communication is a promising application of chaos theory and nonlinear dynamics. In this research, a chaotic algorithm for the new chaotic chameleon system was proposed, studied, and implemented. The chameleon chaotic system has been preferred to be employed because it has the property of changing from self-excited (SA) to hidden-attractor (HA) which increases the complexity of the system dynamics and gives strength to the encryption algorithm. A chaotic chameleon system is one in which, depending on the parameter values, the chaotic attractor alternates between being a hidden attractor and a self-excited attractor. This is an important feature, so it is preferable to use it in cryptography compared to other types of chaotic systems. This model was first implemented using a Field Programmable Gate Array (FPGA), which is the first time it has been implemented in practical applications. The chameleon system model was implemented using MATLAB Simulink and the Xilinx System Generator model. Self-excited, hidden, and coexisting attractors are shown in the proposed system. Vivado software was used to validate the designs, and Xilinx ZedBoard Zynq-7000 FPGA was used to implement them. The dynamic behavior of the proposed chaotic system was also studied and analysis methods, including phase portrait, bifurcation diagrams, and Lyapunov exponents. Assessing the quality of the suggested method by doing analyses of many quality measures, including correlation, differential signal-to-noise ratio (SNR), entropy, histogram analysis, and spectral density plot. The numerical analyses and simulation results demonstrate how well the suggested method performs in terms of security against different types of cryptographic assaults.

Symmetry of chaotic attractors and kink-antikink structures in CMLs

Integer and fractional order analysis of a 3D system and generalization of synchronization for a class of chaotic systems

Adaptive synchronization between chaotic dynamical systems of different order

Objectives This study proposes a novel numerical scheme for solving a new class of chaotic systems, with particular focus on the stochastic fractional-order Lorenz system (SFLS). The objective is to enhance the modeling and analysis of SFLS under a fractional framework while investigating the dynamical effects of multiplicative white noise. Materials and Methods The SFLS is formulated using the Atangana–Baleanu–Caputo fractional derivative. A robust numerical algorithm is developed to obtain approximate solutions of the system in the presence of multiplicative white noise. The performance and validity of the proposed method are demonstrated through comprehensive two-dimensional (2D) and three-dimensional (3D) numerical simulations. Results The computational results confirm that the proposed scheme accurately captures the stochastic and chaotic dynamics of the fractional-order Lorenz system. The simulations illustrate the significant influence of multiplicative white noise on system trajectories and stability characteristics. The method exhibits reliability, stability, and computational efficiency in approximating the system’s behavior. Conclusion The proposed numerical framework provides an effective tool for analyzing stochastic fractional chaotic systems. The findings contribute to improved modeling and prediction of noise-driven chaotic phenomena, with potential applications in climate and weather modeling, engineering systems, and economic forecasting where stochastic perturbations play a critical role.

Chaotic systems are nonlinear dynamic systems, the main feature of which is high sensitivity to initial conditions. To initiate a design process in fuzzy model, chaotic systems must first be represented by T-S fuzzy models. In this paper, a new fuzzy modeling method based on sector nonlinearity approach has been recommended for chaotic systems relating to initial condition variations using the interval type-2 Takagi–Sugeno (IT2 T-S) fuzzy model. Examining many famous chaotic systems, it can be seen that nonlinear terms in chaotic systems are composed of just one variable or more. In the process of constructing an IT2 T-S fuzzy model which represents the chaotic systems, authors will focus on nonlinear terms of the chaotic systems. The proposed interval type-2 Takagi-Sugeno fuzzy modeling method is employed for two kinds of nonlinear terms; at first, a uni-variable nonlinear term is presented and then a multi-variable one will be introduced. So, it will be shown how many famous chaotic systems are represented by IT2 T-S fuzzy model. Then the proposed approach is applied to Genesio-Tesi and Rossler systems. Numerical simulations are given to demonstrate the efficiency of the proposed method in MATLAB environment.