Chaos (Physics)

"Physics and Catholicism"

by Philippe Gagnon

Forthcoming in Encyclopedia of Sciences and Religions, Nina P. Azari and Anne Runehov (Eds.) (Berlin: Springer, forthcoming in 2013). (ISBN 978-1-4020-8264-1)

Outline: The reality of Catholicism; The question of the development of science; Historical outlook at some... more Outline: The reality of Catholicism; The question of the development of science; Historical outlook at some transitional moments; When dogma meets science; Contemporary physics and the worldview of Catholicism; Awaiting a 'Grand Narrative' and the final vision of harmony.

Phenomenological Sociography and Time Travel

by Peter Theodoropoulos

Related to questions of Time, structure and aspectual dimensions of relational time. Related theories that I am working on to discuss this are syntactogenerics and syntactogenesis, Syntacto generics and Semanto Generics, Syntactogenesis and Semantogenesis relations, and the nature of time as emminative, immanent and transcendent meaning both virtual and ontological. Please offer your input if you so wish.

What is time? How is time non linear? What are the relational or assemblages of subjective structure, how can we... more What is time? How is time non linear? What are the relational or assemblages of subjective structure, how can we create a taxonomy of types of relational time? By what features does time seem linear, and what is the nature of conditioning, or ritual space that instantiates regularities IN the mind? How is this relation both physical and immaterial? IS there such thing as the immaterial? Can time be said to be Immaterial and materializable? Is time instantiative or phasic, normative and bound to rules or flexible? How do we understand distinctions in subjective and objective time, how can we quantify and compare and contrast variables of each? Is there such thing as a phase shift in which ontological bias may be met with nomological or noumenal objectivity, if so what are the expectations, means of discernment and systems available to explore critique, modify and experiment with time relations? What, finally, are some means to codify and structure simulations of these relations utilizing electromagnetic fields that may interface with the Neural correlates of Consciousness study to explore results? What should our ethical considerations with regards to this sort of study be? How was your day?

Chaotic mixing of granular material in slowly rotating containers as a discrete mapping

by Alexander Vikhansky

This theme issue on Multistability in Dynamical Systems provides a state-of-the-art pre-sentation on the subject. It comprises several ongoing contributions and …

by Alexander N. Pisarchik

VIDEO ENCRYPTION WITH CHAOTICALLY COUPLED CHAOTIC MAPS USING DMP-6437 AND SIMULINK

by Alexander N. Pisarchik

R. JAIMES-REATEGUI, EMMANUEL VALDES JARAMILLO, RICARDO SEVILLA-ESCOBOZA, JUAN HUGO GARCÍA LOPEZ, CARLOS E. CASTAÑEDA HERNANDEZ, GUILLERMO HUERTA-CUELLAR, AND D. LOPEZ-MANCILLA, MASSIMILIANO ZANIN AND ALEXANDER N. PISARCHIK
1st International Congress on Instrumentation and Applied Sciences, Cancun, Mexico, October 26-29, 2010

To encrypt video we use a secure cryptosystem for direct encryption of color images in each frame of a video, based on... more To encrypt video we use a secure cryptosystem for direct encryption of color images in each frame of a video, based on chaotically coupled chaotic maps, that provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels colors, using a DMP (Digital Media Processor) we process video, separate it in 3 components RGB (Red, Green, Blue) and apply our algorithm for encryption or decryption.

Control of laser dynamics

by Alexander N. Pisarchik

A.N. Pisarchik, Control of laser dynamics – art. no. 60462H, Proc. SPIE 6046, H462-H462 (2006). Proceedings of SPIE, Volume 6046, Fifth Symposium Optics in Industry, Eric Rosas, Rocío Cardoso, Juan C. Bermudez, Oracio Barbosa-García, Eds., February 2006, 60462H (Feb. 10, 2006), 9 p. ISBN: 9780819460790. Congress: 8-9 September, 2005, Santiago, Querétaro, Mexico.

Secure Computer Communication Based on Chaotic Rössler Oscillators

by Alexander N. Pisarchik

J.H. García-López, R. Jaimes-Reategui, R. Chiu-Zarate, D. Lopez-Mancilla, R. Ramirez-Jimenez, and A.N. Pisarchik, The Open Electrical and Electronic Engineering Journal, 2008, 2, 41-44

We describe a communication scheme based on chaotic Rössler oscillators for transmission of secure messages via... more We describe a communication scheme based on chaotic Rössler oscillators for transmission of secure messages via computers. The computers are synchronized through one of the channels via one of the variables of the Rössler system, while an information signal is transmitted through another channel by adding the message to another system variable. This scheme provides more stable communication because the information signal does not enter to the receiver and hence does not cause an error in synchronization. The method is tested with different types of information signals: audio, text, and image.

Control of Multistability in a Directly Modulated Diode Laser

by Alexander N. Pisarchik

A. N. Pisarchik and B. F. Kuntsevich, IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 38, NO. 12, DECEMBER 2002

A semiconductor laser with modulated injection current has the property that many competing behaviors are possible and... more A semiconductor laser with modulated injection current has the property that many competing behaviors are possible and the system tends to alternate among them. Such a situation is not desirable if a stable output is required.We show with numerical simulations that additional slow harmonic modulation can annihilate undesirable coexisting attractors in this laser. We demonstrate great flexibility of the method in manipulating the laser’s dynamics to select a desired behavior and even to make the system monostable.

Nonlinear amplitude-detuning characteristic of a CO2 laser with modulated losses

by Alexander N. Pisarchik

A complex numerical study of the evolution of the nonlinear response of a CO2 laser with harmonic and biharmonic loss... more A complex numerical study of the evolution of the nonlinear response of a CO2 laser with harmonic and biharmonic loss modulations has been performed with allowance for cavity detuning. We have found that the laser response has specific features which are unambiguously defined by the relationship between the frequency of the loss modulation and the fundamental resonance frequency of the laser.

Homoclinic orbits in a piecewise linear Rössler-like circuit

by Alexander N. Pisarchik

In addition to the well-known Rössler funnel that consists in near-homoclinic orbits, perfect homoclinic orbits have... more In addition to the well-known Rössler funnel that consists in near-homoclinic orbits, perfect homoclinic orbits have been found numerically and experimentally in a simplest piecewise linear Rössler-like electronic circuit. The evolution of the system in the homoclinic range exhibits period-bubbling and period-adding cascades when a control parameter is changed. A scaling law in the period-adding cascade between the period of a homoclinic orbit and the bifurcation parameter is evaluated. Other phenomena, such as the coexistence of two homoclinic orbits, homoclinic chaos, symmetry breaking and phase bistability are also demonstrated. The results of numerical simulations are in a good agreement with experiments.

Synchronization of Multistable Systems

by Alexander N. Pisarchik

We present the detailed study of synchronization of two unidirectionally coupled identical systems with coexisting... more We present the detailed study of synchronization of two unidirectionally coupled identical systems with coexisting chaotic attractors and analyze system dynamics observed on the route from asynchronous behavior to complete synchronization when the coupling strength is increased. We distinguish three stages of synchronization depending on the coupling strength which can be conventionally divided into three intervals. A relatively weak coupling induces asynchronous intermittent jumps between coexisting attractors and anticipating phase synchronization within windows where the systems stay in similar attractors; an intermediate coupling creates combined attractors that give rise to generalized synchronization in the form of subharmonic frequency entrainment; and a strong coupling results in complete synchronization. The results of numerical simulations are in good agreement with experiments carried out with piecewise- linear Rossler-like electronic circuits.

Shift of attractor boundaries in a system with a slow harmonic parameter perturbation

by Alexander N. Pisarchik

A.N. Pisarchik and R. Corbalán
Physica D 150 (2001) 14–24

In a dynamical system with coexisting attractors, a slow periodic modulation of a control parameter deforms attractor... more In a dynamical system with coexisting attractors, a slow periodic modulation of a control parameter deforms attractor
boundaries by shifting saddle-node and inverse period-doubling bifurcation points. Dynamical properties of these points are studied numerically and experimentally in a loss-driven CO2 laser with additional slow modulation of the cavity losses. Shifted positions of the bifurcation points depend on the amplitude and frequency of the control modulation. The new position of the saddle-node bifurcation point obeys a particular scaling law for small modulation frequencies and amplitudes.

Secure Computer Communication Based on Chaotic Rössler Oscillators

by Alexander N. Pisarchik

J.H. García-López, R. Jaimes-Reategui, R. Chiu-Zarate, D. Lopez-Mancilla, R. Ramirez-Jimenez, and A.N. Pisarchik, The Open Electrical and Electronic Engineering Journal, 2008, 2, 41-44

We describe a communication scheme based on chaotic Rössler oscillators for transmission of secure messages via... more We describe a communication scheme based on chaotic Rössler oscillators for transmission of secure messages via computers. The computers are synchronized through one of the channels via one of the variables of the Rössler system, while an information signal is transmitted through another channel by adding the message to another system variable. This scheme provides more stable communication because the information signal does not enter to the receiver and hence does not cause an error in synchronization. The method is tested with different types of information signals: audio, text, and image.

Time series prediction using supervised learning and tools from chaos theory

by Andrew Edmonds

Nov. 1996 Ph.D. thesis at the University of Bedfordshire (Previously Luton)

In this work methods for performing time series prediction on complex real
world time series are examined. In... more In this work methods for performing time series prediction on complex real
world time series are examined. In particular series exhibiting non-linear or
chaotic behaviour are selected for analysis. A range of methodologies based
on Takens’ embedding theorem are considered and compared with more
conventional methods. A novel combination of methods for determining the
optimal embedding parameters are employed and tried out with multivariate
financial time series data and with a complex series derived from an
experiment in biotechnology. The results show that this combination of
techniques provide accurate results while improving dramatically the time
required to produce predictions and analyses, and eliminating a range of
parameters that had hitherto been fixed empirically. The architecture and
methodology of the prediction software developed is described along with
design decisions and their justification. Sensitivity analyses are employed to
justify the use of this combination of methods, and comparisons are made
with more conventional predictive techniques and trivial predictors showing
the superiority of the results generated by the work detailed in this thesis.

Finite time stabilization of chaotic systems via single input

by Dr Uchechukwu Vincent

Published in Phys. Lett. A 375 (2010) 119-124

In this Letter, we propose a single control input approach for stabilizing three-dimensional chaotic systems in a... more In this Letter, we propose a single control input approach for stabilizing three-dimensional chaotic systems in a finite time. The method is more general and is derived from the finite-time stability theory and adaptive control technique; and can stabilize almost all well-known three-dimensional chaotic systems without a prior knowledge of the feedback gain. To show the wider applicability of our method, we give illustrations using different chaotic systems with different structure. Numerical simulations are also used to verify the effectiveness of the technique.


Keywords: Chaos; Chaos control; Finite time stabilization

Controlling current reversals in synchronized underdamped ratchets

by Dr Uchechukwu Vincent

Published in J. Physics A: Mathematical and Theoretical 40(16), 165101 (2010)

A pair of underdamped ratchets, coupled via a perturbed asymmetric potential, is shown to make a transition to a fully... more A pair of underdamped ratchets, coupled via a perturbed asymmetric potential, is shown to make a transition to a fully synchronized state wherein stable controlled transport is achieved when the coupling strength exceeds a threshold at which the collective dynamics is attained. This transition to collective transport is connected to a chaos-periodic / quasiperiodic bifurcation in which current reversal is completely eliminated. Based on the Lyapunov stability theory and linear matrix inequalities, we give some necessary and sufficient criteria for stable controlled transport and obtain an exact analytic estimate of the threshold (kth) for the onset of stable controlled current.

A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems

by Dr Uchechukwu Vincent

Published in Communications in Nonlinear Science and Numerical Simulations 14 (2009) 3925–3932

In this paper, a simple adaptive feedback control is proposed for full and reduced-order synchronization of... more In this paper, a simple adaptive feedback control is proposed for full and reduced-order synchronization of time-varying and strictly uncertain chaotic systems. Our method uses only one feedback gain with parameter adaptation law and converges very fast even in the presence of noise. For full synchronization, a drive-response system consisting of two second-order identical parametrically excited oscillators achieve global synchronization;
while for reduced-order synchronization, the dynamical evolution of a second-order parametrically driven oscillator is synchronized with the projection of a third-order time-varying chaotic system. The effectiveness of our approach is demonstrated using numerical simulations.

Synchronization, multistability and basin crisis in coupled pendula

by Dr Uchechukwu Vincent

Published in Journal of Sound and Vibration 329 (2010) 443–456

The synchronization dynamics of two linearly coupled pendula is studied in this paper. Based on the Lyapunov stability... more The synchronization dynamics of two linearly coupled pendula is studied in this paper. Based on the Lyapunov stability theory and Linear matrix inequality (LMI); some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling kth, for the on-set of full synchronization is obtained. The numerical value of kth determined from the average energies of the systems is in good agreement with theoretical analysis. Prior to the on-set of synchronization, the boundary crisis of the chaotic attractor is identified. In the bistable states, where two asymmetric periodic attractors co-exist, it is shown that the coupled pendula can attain multistable states via a new dynamical transition—the basin crisis that occur prior to the on-set of stable synchronization. The essential feature of basin crisis is that the two co-existing attractors are destroyed while new three or more co-existing attractors of the same or different periodicity are created. In addition, the linear perturbation technique and the Routh–Hurwitz criteria are employed to investigate the stability of steady states, and clearly identify the different types of bifurcations likely to be encountered. Finally, two-parameter phase plots, show various regions of chaos, hyperchaos and periodicity.

Synchronization of chaos in RCL-shunted Josephson junction using a simple adaptive controller

by Dr Uchechukwu Vincent

Published in Physica Scripta 79, 035801 (2009)

In this paper, a simple adaptive control is proposed for the synchronization of chaotic dynamics of... more In this paper, a simple adaptive control is proposed for the synchronization of chaotic dynamics of resistive–capacitive–inductive-shunted Josephson junctions (RCLSJ). The synchronization problem is investigated based on a drive–response system configuration consisting of two identical RCLSJ with and without identical system parameters. In addition, the synchronization when the system parameters are unknown is considered based on adaptive parameter control estimation. Sufficient conditions for global asymptotic synchronization are given and numerical simulations are employed to demonstrate the efficiency of the adaptive control scheme. In the presence of noise, we also show that the synchronization is robust and discuss the implication of our adaptive control technique in rapid single flux quantum (RSFQ) devices.

Current reversals and synchronization in coupled ratchets

by Dr Uchechukwu Vincent

Published in Physical Review E 82, 046208 (2010)

Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical... more Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k_th, a specific driving amplitude a_opt is found for which the transport is optimum.