Extension of Lorenz Unpredictability

It is found that Lorenz systems can be unidirectionally coupled such that the chaos expands from the drive system. This is true if the response system is not chaotic, but admits a global attractor, an equilibrium or a cycle. The extension of sensitivity and period-doubling cascade are theoretically proved, and the appearance of cyclic chaos as well as intermittency in interconnected Lorenz systems are demonstrated. A possible connection of our results with the global weather unpredictability is provided.Comment: 32 pages, 13 figure

Chaos in a Discrete Delay Population Model

This paper is concerned with chaos in a discrete delay population model. The map of the model is proved to be chaotic in the sense of both Devaney and Li-Yorke under some conditions, by employing the snap-back repeller theory. Some computer simulations are provided to visualize the theoretical result

Chaotification as a Means of Broadband Vibration Energy Harvesting with Piezoelectric Materials

Computing advances and component miniaturization in circuits coupled with stagnating battery technology have fueled growth in the development of high efficiency energy harvesters. Vibration-to-electricity energy harvesting techniques have been investigated extensively for use in sensors embedded in structures or in hard-to-reach locations like turbomachinery, surgical implants, and GPS animal trackers. Piezoelectric materials are commonly used in harvesters as they possess the ability to convert strain energy directly into electrical energy and can work concurrently as actuators for damping applications. The prototypical harvesting system places two piezoelectric patches on both sides of the location of maximum strain on a cantilever beam. While efficient around resonance, performance drops dramatically should the driving frequency drift away from the beam\u27s fundamental frequency. To date, researchers have worked to improve harvesting capability by modifying material properties, using alternative geometries, creating more efficient harvesting circuits, and inducing nonlinearities. These techniques have partially mitigated the resonance excitation dependence for vibration-based harvesting, but much work remains. In this dissertation, an induced nonlinearity destabilizes a central equilibrium point, resulting in a bistable potential function governing the cantilever beam system. Depending on the environment, multiple stable solutions are possible and can coexist. Typically, researchers neglect chaos and assume that with enough energy in the ambient environment, large displacement trajectories can exist uniquely. When subjected to disturbances a system can fall to coexistent lower energy solutions including aperiodic, chaotic oscillations. Treating chaotic motion as a desirable behavior of the system allows frequency content away from resonance to produce motion about a theoretically infinite number of unstable periodic orbits that can be stabilized through control. The extreme sensitivity to initial conditions exhibited by chaotic systems paired with a pole placement control strategy pioneered by Ott, Grebogi, and Yorke permits small perturbations to an accessible system parameter to alter the system response dramatically. Periodic perturbation of the system trajectories in the vicinity of isolated unstable orbit points can therefore stabilize low-energy chaotic oscillations onto larger trajectory orbits more suitable for energy harvesting. The periodic perturbation-based control method rids the need of a system model. It only requires discrete displacement, velocity, or voltage time series data of the chaotic system driven by harmonic excitation. While the analysis techniques are not fundamentally limited to harmonic excitation, this condition permits the use of standard discrete mapping techniques to isolate periodic orbits of interest. Local linear model fits characterize the orbit and admit the necessary control perturbation calculations from the time series data. This work discusses the feasibility of such a method for vibration energy harvesting, displays stable solutions under various control algorithms, and implements a hybrid bench-top experiment using MATLAB and LabVIEW FPGA. In conclusion, this work discusses the limitations for wide-scale use and addresses areas of further work; both with respect to chaotic energy harvesting and parallel advances required within the field as a whole

Adaptive Sliding Mode Control of Chaos in Permanent Magnet Synchronous Motor via Fuzzy Neural Networks

In this paper, based on fuzzy neural networks, we develop an adaptive sliding mode controller for chaos suppression and tracking control in a chaotic permanent magnet synchronous motor (PMSM) drive system. The proposed controller consists of two parts. The first is an adaptive sliding mode controller which employs a fuzzy neural network to estimate the unknown nonlinear models for constructing the sliding mode controller. The second is a compensational controller which adaptively compensates estimation errors. For stability analysis, the Lyapunov synthesis approach is used to ensure the stability of controlled systems. Finally, simulation results are provided to verify the validity and superiority of the proposed method

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS

From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare