Edmon Perkins

LAB2701

https://dergipark.org.tr/en/pub/chaos/issue/80150

https://dergipark.org.tr/en/pub/chaos/issue/77246

The Hopf oscillator is a nonlinear oscillator that exhibits limit cycle motion. This reservoir computer utilizes the vibratory nature of the oscillator, which makes it an ideal candidate for reconfigurable sound recognition tasks. In this paper, the capabilities of the Hopf reservoir computer performing sound recognition are systematically demonstr...

The van der Pol oscillator has historical and practical significance to spiking neural networks. It was proposed as one of the first models for heart oscillations, and it has been used as the building block for spiking neural networks. Furthermore, the van der Pol oscillator is also readily implemented as an electronic circuit. For these reasons, w...

Shape memory alloys are metal alloys that have multiple crystalline states, which can be accessed through heating and cooling. These actuators have several attractive properties, such as a high strength-to-weight ratio, robustness, and compact structure. Added to this, shape memory alloys have a self-sensing property. However, shape memory alloy wi...

A self-sensing shape memory alloy actuator is harnessed as a computational resource by utilizing it as a physical reservoir computer. Physical reservoir computing is a machine learning technique that takes advantage of the dynamics of a physical system for computation. Compared to recurrent neural networks, this architecture can be both fast and ef...

https://dergipark.org.tr/en/pub/chaos/issue/75756

Adaptive oscillators are a subset of nonlinear oscillators that can learn and encode information in dynamic states. By appending additional states onto a classical Hopf oscillator, a four-state adaptive oscillator is created that can learn both the frequency and amplitude of an external forcing frequency. Analog circuit implementations of nonlinear...

Adaptive oscillators can learn and encode information in dynamic, plastic states. The pendulum has recently been proposed as the base oscillator of an adaptive system. In a mechanical setup, the horizontally forced pendulum adaptive frequency oscillator seeks a resonance condition by modifying the length of the pendulum's rod. This system stores th...

The Hopf oscillator is a nonlinear oscillator that exhibits limit cycle motion. This reservoir computer utilizes the vibratory nature of the oscillator, which makes it an ideal candidate for reconfigurable sound recognition tasks. In this paper, the capabilities of the Hopf reservoir computer performing sound recognition are systematically demonstr...

The Duffing oscillator array has been extensively studied in the context of localization phenomena. By using the nonlinear dynamics of a physical system, machine learning can unlock computational ability from these physical systems. The Duffing oscillator array can be used as a reservoir computer, and multiple benchmark tasks were used to quantify...

https://dergipark.org.tr/en/pub/chaos/issue/73033

Adaptive oscillators are a type of nonlinear oscillator that are capable of learning and storing information in plastic states. Here, a typical mechanical pendulum is modified to have an adjustable rod length to create a pendulum adaptive frequency oscillator. Since the resonance frequency of the pendulum is a function of the rod length, this allow...

Dynamical systems, which are described by differential equations, can have an enhanced response because of their nonlinearity. As one example, the Duffing oscillator can exhibit multiple stable vibratory states for some external forcing frequencies. Although discrete systems that are described by ordinary differential equations have helped to build...

Shape memory alloys (SMAs) can contract their length via a crystalline phase transition that is dependent upon their temperature and stress state. SMAs have been used as linear micro-actuators due to their high strength to weight ratio and compact structure. However, the relatively low linear contraction ([Formula: see text]4%–5% in length) limits...

A discrete element method simulator is developed, which models all of the components (bones, tendons, and ligaments) as discrete elements. This simulator is then used to simulate the dynamics of a raptor’s hallux digit as a case study. The biomechanical linkage is constructed from computerized tomography (CT) scans of bones. The ligaments and tendo...

This issue is dedicated to the memory of Prof. Tenreiro Machado. https://dergipark.org.tr/en/pub/chaos/issue/64884

Although not studied extensively, adaptive frequency oscillators (AFOs) could have many useful applications. AFOs possess the capability of synchronizing their oscillating frequency with their input frequency. Here, the noise-influenced dynamics of the Hopf Adaptive Frequency Oscillator (HAFO) are analyzed in a probabilistic manner. By adding a sto...

A method for true random number generation by directly sampling a high frequency chaotic jerk circuit is explored. A method for determination of the maximum Lyapunov exponent, and thus the maximum bit rate for true random number generation, of the jerk system of interest is shown. The system is tested over a wide range of sampling parameters in ord...

Limit cycle oscillators have the potential to be resourced as reservoir computers due to their rich dynamics. Here, a Hopf oscillator is used as a physical reservoir computer by discarding the delay line and time-multiplexing procedure. A parametric study is used to uncover computational limits imposed by the dynamics of the oscillator using parity...

Often, the responses of additive manufactured parts are studied only in the context of static loads, since most consumer-grade additive manufactured parts are not capable of supporting dynamic loads. Here, the effects of fabrication parameters on the vibratory properties of 3D-printed polymer composite beams were studied. A total of 420 vibratory s...

Physical reservoir computing utilizes a physical system as a computational resource. This nontraditional computing technique can be computationally powerful, without the need of costly training. Here, a Hopf oscillator is implemented as a reservoir computer by using a node-based architecture; however, this implementation does not use delayed feedba...

Reservoir computing was recently proposed as a bio-inspired, machine learning-based computing framework. Though the concept is derived from neural networks, the uniqueness and major significance of this computing technique is that it requires less computational power and follows a much simpler training procedure. Previously, delayed feedback system...

This paper explores the stochastic dynamics of a Hopf adaptive frequency oscillator when driven by noise. Adaptive oscillators are nonlinear oscillators that store information via plastic states. As noise is ubiquitous in physical systems, it is important to gain an understanding of the stochastic effects on adaptive oscillators. Previously, it has...

Since most sporting injuries occur at the lower extremity (50% to 66%) and many of those injuries occur at the knee (30% to 45%), it is important to have robust metrics to measure risk of knee injury. Dynamic measures of knee stability are not commonly used in existing metrics but could provide important context to knee health and improve injury sc...

Typically, nonlinearity is considered to be problematic and sometimes can lead to dire consequences. However, the nonlinearity in a Duffing oscillator array can enhance its ability to be used as a reservoir computer. Machine learning and artificial neural networks, inspired from the biological computing framework, have shown their immense potential...

Adaptive oscillators (AOs) are nonlinear oscillators with plastic states that encode information. Here, an analog implementation of a four-state adaptive oscillator, including design, fabrication, and verification through hardware measurement, is presented. The result is an oscillator that can learn the frequency and amplitude of an external stimul...

Mechanical vibration isolation is an important element for many traditional MEMS devices, (e.g., MEMS inertial sensors and micro-optics) that are deployed in harsh environments (e.g., aerospace applications or automotive applications). Without suitable vibration isolation, environmental vibrations can potentially damage these devices. Micro-scale m...

An alternative approximate implementation of an exactly solvable chaotic oscillator circuit is presented. In this implementation, the previously used op amp based NIC sinusoidal oscillator subcircuit was replaced with a single BJT Colpitts oscillator subcircuit. Although this change resulted in an increase in the order of the chaotic system and int...

Objective To compare the biomechanical properties and healing of ventral midline celiotomies (VMC) closed with a self‐locking knot combination and forwarder start and Aberdeen end (F‐A) vs a traditional knot combination and surgeon's start and end (S‐S). Study design In vivo, experimental. Animals Twenty‐one horses. Methods Fourteen horses under...

The asphaltophone is a musical instrument consisting of (1) a specially designed road surface topology, (2) the tire's contact patch, and (3) the vehicle itself. Each of these components in the asphaltophone has an analogy in the phonograph, which is composed of (1) a record, (2) a stylus, and (3) an amplification device. Asphaltophones are an enjo...

Statically-loaded 2D trusses are the introduction to mechanical engineering courses for nearly every student. Visualization of forces within trusses can often create problems in communicating concepts to students. The 3D printed 2D Truss Demonstration was created to aid in visualizing forces and to provide a modular system with the ability to creat...

The dynamics of a slider-crank mechanism is developed using Kane's equations of motion. The motor torque is a function of the derivative of the generalized coordinate. The nonlinear equations of motion are solved using MATLAB numerical techniques. The sample entropy is calculated for different angular velocities of the crank.

We present a scheme for true random number generation by directly sampling a chaotic jerk system. A method for determination of the maximum Lyapunov exponent, and thus the maximum bit rate for true random number generation, of the jerk system of interest is shown. The system is tested over a wide range of sampling parameters in order to simulate po...

A neural-adaptive trajectory tracking control strategy is proposed for an underwater vehicle manipulator system (UVMS). A feedback term based on a nominal dynamic model is used, and an adaptive neural network is utilized to approximate parametric uncertainties. The performance of this control scheme is demonstrated by applying it to a specific traj...

High temperature applications exists where AC voltage generation would be useful, but the operating temperature is too high for many semiconductor electronic devices to operate reliably. Micromachined Si devices can operate at these elevated temperatures. The nonlinear characteristics of the MEMS parallel plate actuator can be exploited to realize...

The dynamics of a slider-crank mechanism is developed using Kane's equations of motion. The motor torque is a function of the derivative of the generalized coordinate. The nonlinear equations of motion are solved using MATLAB numerical techniques. The sample entropy is calculated for different angular velocities of the crank.

This paper presents a shape memory alloy actuator design using a bimorph structure capable of high-speed actuation and low power consumption. Two active layers of shape memory alloy wires are separated by a passive layer of thermoplastic polyurethane. This structure results in a bending actuator when current is alternated between the two active sha...

In 1995, Steen Krarup Jensen and Jakob Freud-Magnus invented the asphaltophone (also known as a "musical road"). This musical instrument is composed of a 1) road with a specially designed surface topology and 2) a vehicle. To play the instrument, a vehicle is driven across the road at a particular speed; the surface topology of the road causes the...

The modern piano has remained largely unchanged since the 1800s. The currently used piano and its tonal system evolved through science and engineering advancements; its current form has subtle and obvious implications to Western music, such as its equal-tempered tonality. The modern piano is a popular instrument, but it has several obvious limitati...

Time series data were collected from parts of different elements of music. The samples were analyzed using phase plane, Poincaré maps, and Lyapunov exponents. The largest Lyapunov exponent can be used to classify parts of the music elements from the same or different genre.

Nonlinearities in arrays of discrete oscillators can cause energy localizations called intrinsic localized modes (ILMs). Two spatial physical manifestations of localization within the array are the ST-mode ILM (a symmetric mode) and the P-mode ILM (an asymmetric mode). The free response and forced response of the asymmetric vibratory P-mode are dis...

In this paper, an electronic implementation of a non-autonomous nonlinear transistor circuit is presented. This nonlinear circuit topology requires a minimal number of components, which consists of two resistors, two capacitors, and a single NPN bipolar junction transistor (BJT). This topology is of interest because it is relatively simple to const...

Intrinsic localized modes (ILMs) are energy localizations that may occur in arrays of discrete, nonlinear oscillators. When present in physical systems, these energy localizations may cause undesirable dynamics or damaging effects. If properly understood, ILMs may be used to increase the sensing capacity of inertial sensors, store information, or m...

Although 3D printing has become a widespread method of fabrication, the vibratory properties of thermoplastic composites are poorly understood. This is, in part, due to the anisotropies introduced by the 3D printing process, the composite materials used, and the geometry. In this study, an attempt has been made to characterize the vibratory respons...

For stochastic systems, the Fokker-Planck equation (FPE) is used to describe the system dynamics. The FPE is a partial differential equation, which is a function of all the variables in state space and of time. To solve the FPE, several methods are used, including finite elements, moment neglect methods, and cumulant neglect methods. This paper wil...

The influence of noise on the frequency response of the monostable, hardening Duffing oscillator is studied. These changes are studied via the averaged dynamics (using Euler–Maruyama simulations) as well as experiments. It is found that for intermediate noise amplitudes, the qualitative shape of the frequency response curve is changed. For large no...

In arrays of coupled oscillators, intrinsic localized modes are energy localizations, which are caused by nonlinearity and discreteness. Here, the considered array of coupled oscillators is subjected to a combination of sinusoidal excitation and noise excitation. Experimental studies with an array of coupled cantilever oscillators and numerical stu...

In this article, the authors study response localization in coupled arrays of nonlinear oscillators with cubic coupling nonlinearities. For illustration, an array of micro-scale oscillators with intersite or coupling nonlinearities is considered and attention is focused on intrinsic localized modes. Free oscillations and forced oscillations of this...

To utilize noise for systems, which are transmitting or receiving information, the information rate is a necessary metric to consider. The phase lag, which is the difference between the sender (applied forcing) and receiver (the oscillator) phases, has a significant effect on the information rate. However, this phase lag is a nonlinear function of...

Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influenced phenomena and qualitative changes in responses of nonlinear systems with noise are explored. Here, the author considers a range of nonlinear dynamical systems, in...

The effects of noise on transient energy localization in a coupled array of nonlinear oscillators are examined. Results obtained through simulations of deterministic systems are compared to those obtained through Euler-Maruyama scheme based simulations of the corresponding stochastic systems. To complement the numerical studies, a Fokker-Planck for...

While the effects of noise on a dynamical system are often considered to be detrimental, noise can also have beneficial effects on the response of a system. In this work, the vertically excited pendulum is used as an example to illustrate the beneficial effects of noise. The upright equilibrium position of this system can be stabilized passively wi...

Although often considered to be undesirable, noise can produce beneficial effects in a system. Here, the authors discuss two representative nonlinear systems and the influence of noise on the responses of these systems. One of these systems is a set of coupled monostable Duffing oscillators, while the second of these systems is a Rayleigh-Duffing s...