Measurement of small signal variations using one-dimensional chaotic maps

A novel electronic signal Measurement System (MS) based on one-dimensional chaotic maps (Logistic Map (LM) and Tent Map (TM)) has been developed, analysed and tested. Firstly, an in-depth theoretical analysis of each map was performed using MATLAB based computation, and the results demonstrated that the high sensitivity, to initial conditions, of each map was suitable for small signal change detection and measurement. A new 3D representation of chaos map output for varying initial input was also developed allowing the suitability of any one-dimensional chaotic map to be determined. An electronic implementation of the chaotic maps, using low noise and low cost components was developed along with a feedback and a series based MS. The implementations were tested and the experimental results demonstrate a matching within ±1 %, between theory and the electronic implementations, both maps exhibiting behaviour identical to the theoretical maps, ranging from fixed point stability, periodicity and chaos. Each map implementation was tested separately and as part of a complete MS and the results reveal that the proposed measurement technique can detect and measure input signals changes as low as 5 over a 10 V input range, which yields a greater resolution than a MS using an 20 bit Analogue to Digital Converter (ADC) over the same input range. The main advantage of the presented MS is that the accuracy of the measurement is independent of the input range which is not the case with classical approach to measurement based on conditioning circuitry followed by an ADC as the minimum detectable change is directly proportional to the input range

A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters' sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system's attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system's chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator's time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system

Qualitative modeling of chaotic logical circuits and walking droplets: a dynamical systems approach

Logical circuits and wave-particle duality have been studied for most of the 20th century. During the current century scientists have been thinking differently about these well-studied systems. Specifically, there has been great interest in chaotic logical circuits and hydrodynamic quantum analogs. Traditional logical circuits are designed with minimal uncertainty. While this is straightforward to achieve with electronic logic, other logic families such as fluidic, chemical, and biological, naturally exhibit uncertainties due to their inherent nonlinearity. In recent years, engineers have been designing electronic logical systems via chaotic circuits. While traditional boolean circuits have easily determined outputs, which renders dynamical models unnecessary, chaotic logical circuits employ components that behave erratically for certain inputs. There has been an equally dramatic paradigm shift for studying wave-particle systems. In recent years, experiments with bouncing droplets (called walkers) on a vibrating fluid bath have shown that quantum analogs can be studied at the macro scale. These analogs help us ask questions about quantum mechanics that otherwise would have been inaccessible. They may eventually reveal some unforeseen properties of quantum mechanics that would close the gap between philosophical interpretations and scientific results. Both chaotic logical circuits and walking droplets have been modeled as differential equations. While many of these models are very good in reproducing the behavior observed in experiments, the equations are often too complex to analyze in detail and sometimes even too complex for tractable numerical solution. These problems can be simplified if the models are reduced to discrete dynamical systems. Fortunately, both systems are very naturally time-discrete. For the circuits, the states change very rapidly and therefore the information during the process of change is not of importance. And for the walkers, the position when a wave is produced is important, but the dynamics of the droplets in the air are not. This dissertation is an amalgam of results on chaotic logical circuits and walking droplets in the form of experimental investigations, mathematical modeling, and dynamical systems analysis. Furthermore, this thesis makes connections between the two topics and the various scientific disciplines involved in their studies

Synchronization of chaotic systems by using occasional coupling

Ankara : The Department of Electrical and Electronics Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 84-88.Nonlinear and chaotic systems are difficult to control due to their unstable and unpredictable nature. Although, much work has been done in this area, synchronization of chaotic systems still remains a worthwhile endeavor. In this thesis, a method to synchronize systems, inherently operating in a chaotic mode, by using occasional coupling is presented. We assume that a masterslave synchronizing scheme is available. This approach consists of coupling and uncoupling the drive and response systems during some alternated intervals. It is then shown how this synchronization method can be used to transmit information on a chaotic carrier. The applicability of this method will be illustrated using Lorenz system as the chaotic oscillator.Feki, MoezM.S

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

An experimental study of a population of phase-repelling relaxation oscillators

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1995.Includes bibliographical references (leaves 100-103).by Adam Alexander Brailove.Ph.D

Low Power IoT based Automated Manhole Cover Monitoring System as a Smart City application

With the increased population in the big cities, Internet of Things (IoT) devices to be used as automated monitoring systems are required in many of the Smart city’s applications. Monitoring road infrastructure such as a manhole cover (MC) is one of these applications. Automating monitoring manhole cover structure has become more demanding, especially when the number of MC failure increases rapidly: it affects the safety, security and the economy of the society. Only 30% of the current MC monitoring systems are automated with short lifetime in comparison to the lifetime of the MC, without monitoring all the MC issues and without discussing the challenges of the design from IoT device design point of view. Extending the lifetime of a fully automated IoT-based MC monitoring system from circuit design point of view was studied and addressed in this research. The main circuit that consumes more power in the IoT-based MC monitoring system is the analogue to digital converter (ADC) found at the data acquisition module (DAQ). In several applications, the compressive sensing (CS) technique proved its capability to reduce the power consumption for ADC. In this research, CS has been investigated and studied deeply to reach the aim of the research. CS based ADC is named analogue to information converter (AIC). Because the heart of the AIC is the pseudorandom number generator (PRNG), several researchers have used it as a key to secure the data, which makes AIC more suitable for IoT device design. Most of these PRNG designs for AIC are hardware implemented in the digital circuit design. The presence of digital PRNG at the AIC analogue front end requires: a) isolating digital and analogue parts, and b) using two different power supplies and grounds for analogue and digital parts. On the other hand, analogue circuit design becomes more demanding for the sake of the power consumption, especially after merging the analogue circuit design with other fields such as neural networks and neuroscience. This has motivated the researcher to propose two low-power analogue chaotic oscillators to replace digital PRNG using opamp Schmitt Trigger. The proposed systems are based on a coupling oscillator concept. The design of the proposed systems is based on: First, two new modifications for the well-known astable multivibrator using opamp Schmitt trigger. Second, the waveshaping design technique is presented to design analogue chaotic oscillators instead of starting with complex differential equations as it is the case for most of the chaotic oscillator designs. This technique helps to find easy steps and understanding of building analogue chaotic oscillators for electronic circuit designers. The proposed systems used off the shelf components as a proof of concept. The proposed systems were validated based on: a) the range of the temperature found beneath a manhole cover, and b) the signal reconstruction under the presence and the absence of noise. The results show decent performance of the proposed system from the power consumption point of view, as it can exceed the lifetime of similar two opamps based Jerk chaotic oscillators by almost one year for long lifetime applications such as monitoring MC using Li-Ion battery. Furthermore, in comparison to PRNG output sequence generated by a software algorithm used in AIC framework in the presence of the noise, the first proposed system output sequence improved the signal reconstruction by 6.94%, while the second system improved the signal reconstruction by 17.83