Browsing by Subject "Chaos"
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Item Open Access Deterministic phase transitions and self-organization in logistic cellular automata(American Physical Society, 2019) İbrahimi, Muhamet; Gülseren, Oğuz; Jahangirov, SeymurWe present a simple extension in which a single parameter tunes the dynamics of cellular automata (CA) by consequently expanding their discrete state space into a Cantor set. Such an implementation serves as a potent platform for further investigation of several emergent phenomena, including deterministic phase transitions, pattern formation, autocatalysis, and self-organization. We first apply this approach to Conway's Game of Life and observe sudden changes in the asymptotic dynamics of the system accompanied by the emergence of complex propagators. Incorporation of the new state space with system features is used to explain the transitions and formulate the tuning parameter range where the propagators adaptively survive by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, an outer totalistic elementary one-dimensional cellular automaton. In addition, the latter case shows that deterministic transitions between classes of CA can be achieved by tuning a single parameter continuously.Item Open Access A Divine cause for abandoning reason in Shakespeare’s King Lear(Gaziantep Üniversitesi Sosyal Bilimler Enst., 2019) Kurtuluş, GülKing Lear can be considered as one of the most powerful tragedies written by Shakespeare. Written nearly 400 years ago, it appeals to todays’ literary critiques, psychologists and psychiatrists. Shakespeare’s construction of madness is so deep that psychiatrists diagnose the type of madness King Lear suffers from with its various aspects, such as mental disorder, mania, and dementia. One of the elements that triggers his dementia is stress which can be found in Lear’s case due to the corrupted relationship with daughters. Lear has unsolved problems with all of his daughters. Lear does not love them as a father, he loves them as a mother would do hence, their abandonment leads to his collapse. In the father-dominant family model of Elizabethan times King Lear was written, this idea is emphasized in the play further with the exclusion of a mother. King Lear does not only maintain kingly authority but also as the only head of the family and care-giver for his daughters, he maintains both a father’s and mother’s authority role. King Lear does not have a wife to consult when he’s distressed and ask for comfort, however he has his daughters. The play starts off exactly with Lear asking for consolation and love from his daughters. Cordelia’s refusal to give a solid consolation to him results in chaos for Lear who is in desperate need to receive affection. From the very beginning of the play, there is a fight between chaos and order in the kingdom and in King Lear’s mind. In this chaos, madness does not only act as the accelerating power of chaos but also as the remedy of it. In other words, the madness in the play also leads the play back to order. When talking about madness in the play, King Lear and Edgar come to mind as one goes mad and one pretends to be mad. This essay explores King Lear’s madness in the light of new literary studies. It aims to look into the various aspects madness that proceeds from chaos to order through the characters of King Lear and Edgar, and from blindness to healthy eyesight both in metaphoric and literal sense through the characters of King Lear and Gloucester who see better and become wiser in the end.Item Open Access Essays on gene regulatory network models and their stability analysis(Bilkent University, 2023-07) Şener, Dilan ÖztürkGene expression is one of the core areas in comprehending and assessing how biological cells work. Gene regulatory networks (GRNs), representing the intri-cate mechanism between genes and their regulatory modules, are instrumental in controlling gene expression and cell functions. These models shed light on how transcription factors interact with their regulatory modules within a cell. Despite the multitude of studies focusing on the analysis and enhancement of GRNs, there is still room for contributions. This thesis investigates a novel framework inspired by the gene networks constructed using synthetic biology, and presents stability analyses of the nonlinear infinite dimensional dynamical system models arising in this framework. In the first part of the thesis, we extend a previously studied benchmark GRN model including time delay, and present an analysis of the extended frame-work. We utilize unmodeled dynamics and possibly ignored interactions, including higher-order dynamics, in our system design. The stability of the extended system is analyzed by considering various nonlinearity functions and design pa-rameters, and the results are compared with those of the benchmark original model. In the second part, we employ an extension of a gene network model using a multiplicative perturbation of the dynamical system. Each cascaded subsystem in this extended framework has an additional block, including a multiplicative term with a high-pass filter, and the effect of additional parameters on the robustness and delay margin of the system is investigated. Experiments with various design parameters yield that the stability characteristics of GRNs can be improved using the model pertaining to the extension under specific perturbations. Finally, the third part covers the analysis of nonlinear dynamics and chaos in GRNs, particularly focusing on the two-gene original and extended gene net-works. Chaotic dynamics depend strongly on the inclusion of time delays, but the circuit motifs that show chaos differ when both original and extended models are considered. Our results suggest that for a particular higher-order extension of the gene network, it is possible to observe the chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of the modification of the original benchmark model induced by unmodeled dynamics. We argue that regulatory gene circuit models with additional parameters demonstrate non-periodic dynamics much more easily.Item Open Access Model based anticontrol of chaos(IEEE, 2003) Morgül, ÖmerWe will consider model based anticontrol of chaotic systems. We consider both continuous and discrete time cases. We first assume that the systems to be controlled are linear and time invariant. Under controllability assumption, we transform these systems into some canonical forms. We assume the existence of chaotic systems which has similar forms. Then by using appropriate inputs, we match the dynamics of the systems to be controlled and the model chaotic systems.Item Open Access Nanomechanical buckling for applications in nonlinear dynamics(Bilkent University, 2021-07) Demiralp, BerkeThere has not been enough attention on post buckling behavior at nano scale even though it reveals rich nonlinear and chaotic dynamics and has potential to be used on cutting edge sensing, actuation, computation and communication applications. Here, full motion of the nanomechanical buckling, starting from un-buckled position to large deformations at post buckling regime has been precisely measured with error bars of ±7 nm for large deformation regime and ±2.8 nm for √ initial bending, with a noise floor of 38.5 pm/ Hz. Line mode of SEM is used for deflection detection which uses secondary electrons collected from sample and relevant code is developed for data processing. Initial bending, initial buckling and inflection point are well defined which can help us to understand transition to post buckling regime and development of sensors and actuators. Additionally, one well oscillation, double well oscillation and chaotic trajectories are investi-gated using the system as forced double well oscillator. Trajectory plotting is performed with an image processing code which benefits from contrast difference of the device and environment. A new region within double well oscillation regime is observed where motion converts from one well oscillation to double well oscilla-tion which could be a candidate on mechanical computation and communication applications. Also, a preliminary design for synchronized chaos experiments using the same buckling platform is developed. Finally, an optomechanical experimental setup and chip is built for measure-ment of one or multiple NEMS beams. Fiber optic techniques are used for exper-imental setup and grating couplers, ring/racetrack resonators are develoxper-imental setup and grating couplers, ring/racetrack resonators are developed for beam measurements. Critical couplings on multiple devices are observed.Item Open Access On the control of chaotic systems in Lur'e form by using dither(Institute of Electrical and Electronics Engineers, 1999-10) Morgül, Ö.In this paper we propose the application of dither for controlling chaotic systems in the Lur'e form. Dither is a high-frequency periodic signal and has the effect of modifying the nonlinearity for some nonlinear systems. We use piecewise constant dither signals and propose three different methods for the selection of dither parameters. We also present some experimental results.Item Open Access On the control of some chaotic systems by using dither(Elsevier, 1999) Morgül, Ö.In this Letter, we propose the application of dither for controlling chaotic systems in Lur'e form. Dither is a high frequency periodic signal that can be used for stabilization of limit cycles in some type of nonlinear systems. We apply the dither to change some parameters of the system which may determine its behaviour. We also present some simulation results.Item Open Access Plane-wave dynamics of single crystal upconversion optical parametric oscillators(Bilkent University, 1999) Akgün, GülbinThis thesis presents our investigation of the dynamics of single crystal up- conversion optical parametric oscillators (OPO’s). In these devices, parametric generation and sum frequency generation or second harmonic generation processes are simultaneously phase matched in a single crystal for the same direction of propagation. These devices can be categorized depending on the polarization geometries of the interacting fields leading to simultaneous phase matching of the two processes. The dynamics of these OPO’s are analyzed using a discrete dynamical system representation. The dependence of the dynamics of the system on various parameters is investigated by forming bifurcation diagrams. Regions of stable steady state, multistable, periodic and chaotic operation are identified on these diagrams.Item Open Access An RC realization of Chua's circuit family(IEEE, 2000) Morgül, Ö.In this brief, we consider a Wien bridge-based resistance–capacitance ( ) chaotic oscillator. We show that this circuit realizes the well-known Chua’s oscillator under some conditions. We also show that this circuit is linearly conjugate, hence equivalent, to a large class of three-dimensional (3-D) systems when the parameters are appropriately chosen. We also present some experimental results.Item Open Access A switching synchronization scheme for a class of chaotic systems(Elsevier, 2002) Morgül, Ö.; Akgül, M.In this Letter, we propose an observer-based synchronization scheme for a class of chaotic systems. This class of systems are given by piecewise-linear dynamics. By using some properties of such systems, we give a procedure to construct the gain of the observer. We prove various stability results and comment on the robustness of the proposed scheme. We also present some simulation results. © 2002 Elsevier Science B.V. All rights reserved.Item Open Access Wien bridge based RC chaos generator(IET, 1995) Morgül, Ö.A new circuit, which is formed by coupling a Chua diode with a Wien bridge oscillator in parallel, is presented. This circuit contains only resistors, capacitors and operational amplifiers. By choosing element values appropriately, this circuit is shown experimentally to exhibit various forms of chaotic behaviour.