Secure Communication Based on Hyperchaotic Chen System with Time-Delay

This research is partially supported by National Natural Science Foundation of China (61172070, 60804040), Fok Ying Tong Education Foundation Young Teacher Foundation(111065), Innovative Research Team of Shaanxi Province(2013KCT-04), The Key Basic Research Fund of Shaanxi Province (2016ZDJC-01), Chao Bai was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.Peer reviewedPostprin

Stabilizing equilibrium by linear feedback control for controlling chaos in Chen system

Stabilization of a chaotic system in one of its unstable equilibrium points by applying small perturbations is studied. A two-stage control strategy based on linear feedback control is applied. Improvement of system performance is addressed by exploiting the ergodicity of the original dynamics and using Lyapunov stability results for control design. Extension to the not complete observability case is also analyzed.Facultad de Ingenierí

Stabilizing equilibrium by linear feedback control for controlling chaos in Chen system

Stabilization of a chaotic system in one of its unstable equilibrium points by applying small perturbations is studied. A two-stage control strategy based on linear feedback control is applied. Improvement of system performance is addressed by exploiting the ergodicity of the original dynamics and using Lyapunov stability results for control design. Extension to the not complete observability case is also analyzed.Facultad de Ingenierí

Time scale and dimension analysis of a budding yeast cell cycle model

BACKGROUND: The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle. RESULTS: By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen's model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth. CONCLUSION: We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network

Non-Linear Dynamics of a Once-Through Steam Generator

This dissertation presents a new analytical model for the Once-Through Steam Generator (OTSG) which is a component responsible for the primary coolant heat removal and the generation and supply of superheated steam to the turbine of the Pressurized Water Reactor (PWR) manufactured by Babcock & Wilcox (B&W) Co. This new analytical model provides the explanation of the oscillatory phenomenon observed in all PWRs manufactured by B&W that uses the OTSG as part of the steam supply system. It was found that the oscillatory behavior is related to the friction pressure drop caused by the reduction in flow area due to the presence of the metal tube holders. The linear analysis performed has shown a pair of complex conjugate eigenvalues with real negative parts, indicating that the OTSG is stable for small perturbations. The global stability was investigated by the construction of the bifurcation diagram whereby the amplitude of the pressure oscillation was plotted against the friction corrector factor. The bifurcation diagram indicates that the limit cycle is stable within the range of physical values of the friction corrector factor. Power spectral density of the plant data revealed two marked features: a resonance at the frequency of oscillation of the limit cycle and a broadband region preceding the location of the resonance peak. The present model does not reproduce the broadband region. A detailed simulation study of the modulation of the amplitude of a limit cycle both with band limited white noise and chaotic noise has shown that the broadband generated by band limited white noise exhibits a power-law dependence on the frequency whereas the chaotic broadband decreases exponentially with frequency. The broadband obtained in the power spectral density of power plant data presented the latter behavior leading to the conclusion that the OTSG limit cycle is modulated by a chaotic component. Furthermore, the calculation of the Lyapunov exponents using the plant data results in positive values reinforcing the above conclusion. It is also demonstrated in this work that undersampling effects seriously hinder the chaotic signatures. This study has shown that the best criterion to determine the chaotic signature in experimental time series is the frequency dependence of the broadband structure in the signal power spectral density. The originality of this work is two fold. First is the model development that leads to the identification of the causative mechanism for the observed OTSG limit cycle. Second is the novel use of otherwise well established tests in the simulation studies of degraded signals for the identification of chaotic components. The recommendations for future work are the extension of the model to allow for motion of all nodal boundaries rather than just the uppermost nodal limits, study of the interaction between the two steam generators in the plant, study of the dependency of the OTSG model eigenvalues with reactor power, and availability of better quality plant data is stressed

Stabilizing equilibrium by linear feedback control for controlling chaos in Chen system

Stabilization of a chaotic system in one of its unstable equilibrium points by applying small perturbations is studied. A two-stage control strategy based on linear feedback control is applied. Improvement of system performance is addressed by exploiting the ergodicity of the original dynamics and using Lyapunov stability results for control design. Extension to the not complete observability case is also analyzed.Facultad de Ingenierí

Machine Learning with Chaotic Strange Attractors

Machine learning studies need colossal power to process massive datasets and train neural networks to reach high accuracies, which have become gradually unsustainable. Limited by the von Neumann bottleneck, current computing architectures and methods fuel this high power consumption. Here, we present an analog computing method that harnesses chaotic nonlinear attractors to perform machine learning tasks with low power consumption. Inspired by neuromorphic computing, our model is a programmable, versatile, and generalized platform for machine learning tasks. Our mode provides exceptional performance in clustering by utilizing chaotic attractors' nonlinear mapping and sensitivity to initial conditions. When deployed as a simple analog device, it only requires milliwatt-scale power levels while being on par with current machine learning techniques. We demonstrate low errors and high accuracies with our model for regression and classification-based learning tasks.Comment: Manuscript is 13 pages, 4 figures. Supplementary Material is 6 pages, 3 figure