Chaotic model and memory in single calcium-activated potassium channel kinetics

Ion channels are pores formed by proteins and responsible for carrying ion fluxes through cellular membranes. The ion channels can assume conformational states thereby controlling ion flow. Physically, the conformational transitions from one state to another are associated with energy barriers between them and are dependent on stimulus, such as, electrical field, ligands, second messengers, etc. Several models have been proposed to describe the kinetics of ion channels. The classical Markovian model assumes that a future transition is independent of the time that the ion channel stayed in a previous state. Others models as the fractal and the chaotic assume that the rate of transitions between the states depend on the time that the ionic channel stayed in a previous state. For the calcium activated potassium channels of Leydig cells the R/S Hurst analysis has indicated that the channels are long-term correlated with a Hurst coefficient H around 0.7, showing a persistent memory in this kinetic. Here, we applied the R/S analysis to the opening and closing dwell time series obtained from simulated data from a chaotic model proposed by L. Liebovitch and T. Toth [J. Theor. Biol. 148, 243 (1991)] and we show that this chaotic model or any model that treats the set of channel openings and closings as independent events is inadequate to describe the long-term correlation (memory) already described for the experimental data. (C) 2008 American Institute of Physics.

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

De la desintegración Espacial a la Conformación regional en la Sabana de Bogotá. Una Propuesta para el desarrollo de la Ciudad Región en el siglo XXI

El presente trabajo de investigación aborda el tema del desarrollo regional en torno a una gran metrópoli como Bogotá y la Sabana de Bogotá. El crecimiento, expansión y relación con los municipios vecinos. Su entorno territorial; es un tema de discusión que cada día adquiere más fuerza desde hace varias décadas. Bogotá y la Sabana de Bogotá, se consideran en la actualidad como un caso representativo del caótico modelo de expansión urbana y crecimiento demográfico, enfrentado al desarrollo urbano como paradigma de la desigualdad de la ciudad latinoamericana. Son muchos los procesos y conflictos de naturaleza Regional y metropolitana que atraviesa la capital colombiana. Sin embargo esta investigación abordada el tema desde la necesidad de gobernanza y coordinación para el desarrollo territorial consensuado y equilibrado de la Región. La sabana de Bogotá está conformada por ciudades dormitorio, ciudades industriales, turísticas, agropecuarias, etc., es atravesada por el Río Bogotá, y en su centro la gran metrópoli, Bogotá D.C. centro de trabajo muy importante a nivel nacional, su área de influencia más próxima llega hasta: Caqueza, Zipaquira, Facatativa, Soacha, Fusagasuga y Girardot. Principales polos de desarrollo en la sabana y el departamento. Cundinamarca está compuesto por 15 provincias y Bogotá. Conformando un sistema de redes urbanas con necesidades comunes y demanda servicios públicos, de transporte, aseo, movilidad, salud, educación, espacio público y calidad ambiental. La metodología de esta investigación consiste en el análisis de la región a partir de la articulación de planes de ordenamiento territorial en un área de estudio propuesta. Mediante entrevistas con profesionales, expertos, funcionarios y empleados públicos y teniendo en cuenta las posibilidades legales en Colombia para el desarrollo territorial regional, establecer la situación real en materia de desarrollo para el departamento de Cundinamarca, evidenciando las necesidades del territorio y su desarrollo de una forma más compleja, valorando las sinergias y necesidades sociales, ambientales y económicas propias del crecimiento urbano, para proponer una serie de directrices que estructuren un desarrollo regional equilibrado en Bogotá y Cundinamarca. El análisis de los modelos del caso contribuye a fortalecer iniciativas para el desarrollo Regional de la Sabana de Bogotá como territorio sostenible: ambiental, económico y socialmente. En un sistema de redes que interconecte a Bogotá, con Cundinamarca, Colombia y el resto del mundo. Cundinamarca como región debe fijar estrategias y articular políticas en función de un modelo de desarrollo urbano regional para el departamento y la Sabana de Bogotá. Directrices departamentales básicas y fundamentales para el desarrollo territorial equilibrado que promueva ciudades sostenibles, compactas y con Calidad de vida para todos sus habitantes. ABSTRACT: This research addresses the issue of regional development around a big metropolis like Bogotá and Sabana de Bogota. The growth, expansion and relations with neighboring municipalities. Your local environment; It is an issue that becomes stronger every day for decades. Bogotá and Sabana de Bogotá, are considered today as a representative case of the chaotic model of urban expansion and population growth, urban development faced as a paradigm of inequality in Latin American city. Many processes and conflicts of Regional and metropolitan nature that crosses the Colombian capital. However this research addressed the issue from the need for governance and coordination for consensual and balanced territorial development of the region. The savannah of Bogota consists of bedroom communities, industrial cities, tourism, agriculture, etc., is crossed by the Bogota River, and at its center the great metropolis, Bogota DC center very important work at the national level, the area closest influence reaches: Caqueza, Zipaquira, Facatativa, Soacha, Fusagasuga and Girardot. Main centers of development in the savannah and the department. Cundinamarca is composed of 15 provinces and Bogota. Forming a system of urban networks with common needs and demand utilities, transportation, grooming, mobility, health, education, public space and environmental quality. The methodology of this research is the analysis of the region from the joint land use plans in the proposed study area. Through interviews with professionals, experts, public officials and employees and taking into account the legal possibilities in Colombia for regional territorial development, establish the real situation in development for the department of Cundinamarca, showing the region's needs and development of a more complex form, assessing synergies and own social, environmental and economic needs of urban growth, to propose a set of guidelines to structure a balanced regional development in Bogota and Cundinamarca. The analysis of case models helps to strengthen initiatives for regional development of the Sabana de Bogota and sustainable region: environmentally, economically and socially. In a network system that interconnects to Bogotá with Cundinamarca, Colombia and elsewhere. Cundinamarca region should set as joint strategies and policies based on a model of regional urban development for the department and the Sabana de Bogota. Basic and fundamental to balanced territorial development that fosters sustainable, compact and quality of life for all its inhabitants cities departmental guidelines.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving; the equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure. (C) 2004 Elsevier Ltd. All rights reserved.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

Chaotic advection in blood flow

In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.

Chaotic communication based on the particle-in-a-box electronic circuit

A secure communication system based on the error-feedback synchronization of the electronic model of the particle-in-a-box system is proposed. This circuit allows a robust and simple electronic emulation of the mechanical behavior of the collisions of a particle inside a box, exhibiting rich chaotic behavior. The required nonlinearity to emulate the box walls is implemented in a simple way when compared with other analog electronic chaotic circuits. A master/slave synchronization of two circuits exhibiting a rich chaotic behavior demonstrates the potentiality of this system to secure communication. In this system, binary data stream information modulates the bifurcation parameter of the particle-in-a-box electronic circuit in the transmitter. In the receiver circuit, this parameter is estimated using Pecora-Carroll synchronization and error-feedback synchronization. The performance of the demodulation process is verified through the eye pattern technique applied on the recovered bit stream. During the demodulation process, the error-feedback synchronization presented better performance compared with the Pecora-Carroll synchronization. The application of the particle-in-a-box electronic circuit in a secure communication system is demonstrated.

Experimental evidence of frequency entrainment between coupled chaotic oscillations

The nonlinear response of a chaotic system to a chaotic variation in a system parameter is investigated experimentally. Clear experimental evidence of frequency entrainment of the chaotic oscillations is observed. We show that analogous to the frequency locking between coupled periodic oscillations, this effect is generic for coupled chaotic systems.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Stages of chaotic synchronization

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (C) 1998 American Institute of Physics.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.

Control of chaotic instabilities in a spinning spacecraft with dissipation using Lyapunov's method

Control of chaotic instability in a simplified model of a spinning spacecraft with dissipation is achieved using an algorithm derived using Lyapunov's second method. The control method is implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability for a range of forcing amplitudes and frequencies when a sinusoidally varying torque is applied to the spacecraft. Such a torque, may arise in practice from an unbalanced rotor or from vibrations in appendages. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and bifurcation diagrams. (C) 2002 Elsevier Science Ltd. All rights reserved.