Dynamical systems and Chaos

Lawhead - Concepts in Complexity

by Jon Lawhead

About Imperfect Mushroom Billiards

by Karel Zapfe

Novel temporal behavior of a nonlinear dynamical system: The completely inelastic bouncing ball

by Anita Mehta

Bouncing ball with a finite restitution: Chattering, locking, and chaos

by Anita Mehta

Modeling of synchronized bursting events: the importance of inhomogeneity

by Vladislav Volman

Self-regulated homoclinic chaos in neural networks activity

by Vladislav Volman

Interplay between Network Topology and Dynamics in Neural Systems

by Samuel Johnson

PhD thesis
Homepage: http://www.ugr.es/~sam/index_archivos/thesis.pdf
TESEO: https://www.educacion.gob.es/teseo/mostrarSeleccion.do

This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and... more This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems:

1) How the activity of neurons, via synaptic changes, can shape the topology of the network they form part of, and

2) How the resulting network structure, in its turn, might condition aspects of brain behaviour.

Although the emphasis is on neural networks, several theoretical findings which are relevant for complex networks in general are presented - such as a method for studying network evolution as a stochastic process, or a theory that allows for ensembles of correlated networks, and sets of dynamical elements thereon, to be treated mathematically and computationally in a model-independent manner. Some of the results are used to explain experimental data - certain properties of brain tissue, the spontaneous emergence of correlations in
all kinds of networks... - and predictions regarding statistical aspects of the central nervous system are made. The mechanism of Cluster Reverberation is proposed to account for the near-instant storage of novel information the brain is capable of.

New Product Development as a Complex Adaptive System of Decisions

by Ian McCarthy

McCarthy I. P., Tsinopoulos C., Allen P.M & Rose-Anderssen C. 2006. New Product Development as a Complex Adaptive System of Decisions. Journal of Product Innovation Management, 23(5): 437-456.

Early research on new product development (NPD) has produced descriptive frameworks and models that view the process... more Early research on new product development (NPD) has produced descriptive frameworks and models that view the process as a linear system with sequential and discrete stages. More recently, recursive and chaotic frameworks of NPD have been developed, both of which acknowledge that NPD progresses through a series of stages, but with overlaps, feedback loops, and resulting behaviors that resist reductionism and linear analysis. This article extends the linear, recursive, and chaotic frameworks by viewing NPD as a complex adaptive system (CAS) governed by three levels of decision making - in-stage, review, and strategic - and the accompanying
decision rules. The research develops and presents propositions that predict how the configuration and organization of NPD decision-making agents will influence the potential for three mutually dependent CAS phenomena: nonlinearity, selforganization, and emergence. Together these phenomena underpin the potential for NPD process adaptability and congruence. To support and to verify the propositions, this study uses comparative case studies, which show that NPD process
adaptability occurs and that it is dependent on the number and variety of agents, their corresponding connections and interactions, and the ordering or disordering effect of the decision levels and rules. Thus, the CAS framework developed within this article maintains a fit among descriptive stance, system behavior, and innovation type, as it considers individual NPD processes to be capable of switching or toggling between different behaviors - linear to chaotic - to produce corresponding innovation outputs that range from incremental to radical in accord with market expectations.

De l'utilisation d'un oscillateur optoélectronique comme Reservoir Computer

by Yvan Paquot

JNOG 2010

Nous présentons ici l’implémentation optique d’un réseau de neurones artificiel de type reservoir computer. Il est... more Nous présentons ici l’implémentation optique d’un réseau de neurones artificiel de type reservoir computer. Il est réalisé sur une structure d’oscillateur optoélectronique utilisant une boucle à retard en fibre optique. Notre système est étudié en régime libre, puis soumis à des tests standardisés, y compris sa capacité de mémoire, pour mesurer ses performances en tant que reservoir computer.

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?

On the security of a new image encryption scheme based on chaotic map lattices

by David Arroyo

Generation of composed musical structures through recurrent neural networks based on chaotic inspiration - Andrés Coca

by Andrés Eduardo Coca Salazar

Andrés E. Coca, Roseli A. F. Romero, and Liang Zhao

In this work, an Elman recurrent neural network
is used for automatic musical structure composition based onmore In this work, an Elman recurrent neural network
is used for automatic musical structure composition based on
the style of a music previously learned during the training
phase. Furthermore, a small fragment of a chaotic melody is
added to the input layer of the neural network as an inspiration
source to attain a greater variability of melodies. The neural
network is trained by using the BPTT (back propagation through
time) algorithm. Some melody measures are also presented for
characterizing the melodies provided by the neural network and
for analyzing the effect obtained by the insertion of chaotic
inspiration in relation to the original melody characteristics.
Specifically, a similarity melodic measure is considered for
contrasting the variability obtained between the learned melody
and each one of the composite melodies by using different
quantities of inspiration musical notes.

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.