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PubMed1998

The Feigenbaum scenario as a model of the limits of conscious information processing.

The Feigenbaum scenario of the mathematical period doubling sequence from order to deterministic chaos has led to new insights about the nonlinear dynamics of a wide variety of physical and biological systems. Multiple realms from purely mechanical systems, fluid dynamics and weather to the patterns of biological growth and the dynamic of the heart, hormone and brain rhythms have been found to exhibit aspects of the Feigenbaum period doubling sequence. We explore the possibility that the Feigenbaum scenario can be extended to experiences of sensation, perception and human cognition as well. We also review the empirical data that supports the view that the Feigenbaum scenario of the period doubling sequence may portray an important limit in conscious information processing. We conclude that a major function of consciousness may be to transform the nonlinear, irrational and difficult to predict dynamics of unconscious nature into the more linear, rational and predictable psychodynamics that make human experience and social life possible.

Cognition↗

PubMed2005

Complex dynamics in unidirectionally coupled overdamped bistable systems subject to a time-periodic external signal.

Recently, we have studied the emergence of oscillatory behavior in overdamped undriven nonlinear dynamic systems subject to carefully crafted coupling schemes and operating conditions [V. In, Phys. Rev. E 68, 045102(R) (2003).] The theoretical ideas have been validated in an experimental setup of N = 3 coupled ferromagnetic cores subject to a dc external magnetic "target" signal; the oscillations (corresponding to the periodic switching of each core between its stable steady states of magnetization) are triggered when the coupling constant crosses a threshold value, with the oscillation frequency exhibiting a characteristic scaling behavior with the "separation" of the coupling constant from its threshold value, as well as with the external signal amplitude. Here, we consider the system response to a time-periodic signal. We demonstrate experimentally that, depending on the signal amplitude and frequency, the response can be either synchronized to the signal frequency or to one-third this frequency. These phenomena afford unique techniques for time-periodic signal detection and characterization for a large class of sensors.

Journal Article↗

PubMed2002

Endothelial cell dynamics and complexity theory.

OBJECTIVE: To apply complexity theory to understanding endothelial cell function in health and disease. DATA SOURCES AND STUDY SELECTION: Published research and review articles in the English language related to complexity theory and endothelial cell biology. DATA EXTRACTION AND SYNTHESIS: The results of published studies have been used to generate a hypothesis of nonlinear dynamics in endothelial cell biology. CONCLUSIONS: The endothelium displays nonlinear complexity. I propose a model in which healthy endothelium retains a broad range of responses and is therefore highly active, whereas dysfunctional endothelium becomes locked into a narrow range of responses, approaching a single steady state and eventual quiescence. These concepts lay a foundation for understanding the pathophysiology of endothelial cell dysfunction in the multiple organ dysfunction syndrome.

Blood Coagulation↗

PubMed2001

Modeling and inverse simulation of somersaults on the trampoline.

This paper describes a biomechanical model for numerical simulation of front and back somersaults, without twist, performed on the trampoline. The developed mathematical formulation is used to solve an inverse dynamics problem, in which the moments of muscle forces at the joints that result in a given (measured) motion are determined. The nature of the stunts and the way the human body is maneuvered and controlled can be studied. The calculated torques can then be used as control signals for a dynamic simulation. This provides a way to check the inverse dynamics procedures, and influence of typical control errors on somersault performance can be studied. To achieve these goals, the nonlinear dynamical model of the trampolinist and the interacting trampoline bed has been identified, and a methodology for recording the actual somersault performances was proposed. Some results of numerical simulations are reported.

Biomechanical Phenomena↗

PubMed1985

Sex and the emergence of species.

We argue that the existence of species as distinct and relatively homogeneous groupings of individuals is a consequence of the nonlinear dynamics inherent in sexual reproduction. This approach provides an answer to two interrelated problems which Darwin posed and tried to solve. Why are there missing links (i.e. gaps) between species in habitat space, and why are there missing links between species in time as evidenced in the fossil record? A crucial difference between outcrossing sexual organisms (i.e. organisms in which mating is between different individuals) and obligate selfers or parthenogens lies in the dynamic of the underlying replication process. Replication is a linear function of density for obligate selfers or parthenogens but nonlinear for outcrossing sexuals. The non-linearity stems from the simple fact that with outcrossing, two individuals must come together to mate. We argue that this fact leads to density dependent fitness (per capita rate of increase) with an intrinsic disadvantage of low population density. This cost of rarity results in a distribution of distinct species. By establishing the causal connections in evolution between outcrossing sex and the very existence of species as distinct collections of organisms, our account lends theoretical support to a unitary concept of species with interbreeding as the fundamental defining property.

Adaptation, Physiological↗

PubMed2005

Breather-induced anomalous charge diffusion.

We present results on the diffusive motion of a charge interacting with the nonlinear dynamics of a thermalized underlying lattice. Signatures of anomalous diffusive properties are found at relatively high temperatures, where highly nonlinear excitations are present. A sublinear diffusion and a plateau appear before the standard long-time diffusion during the evolution of the mean-squared displacement and a significant degree of heterogeneity is exhibited among individual trajectories. Both properties are connected with the existence of vibrational hot spots (breather or multibreather excitations). Transport parameters of the charge are strongly affected in this case, as can be exemplified by the significant suppression of the diffusion coefficient D. The variation of D with temperature follows a stretched exponential law. The results are contrasted with those of the linearized case, in the absence of breathers. Such anomalous diffusion of a charge coupled to a thermalized lattice may be relevant in low-dimensional soft materials with strong anharmonicities, such as biomolecules, conducting polymers, etc.

Biopolymers↗

PubMed1996

Bistability and its regulation by serotonin in the endogenously bursting neuron R15 in Aplysia.

1. Previous computational studies of models of neuron R15 in Aplysia have indicated that several distinct modes of electrical activity may coexist at a given set of parameters, that this multistability can be modulated by transmitters such as serotonin (5-HT) and that brief perturbations of the membrane potential can induce persistent changes in the mode of electrical activity. To test these predictions, the responses of R15 neurons to injections of brief (1.5 s) current pulses were recorded intracellularly in the absence and presence of 5-HT. 2. In the absence of 5-HT, brief perturbations induced abrupt transitions in the electrical activity from bursting to beating. Such transitions were observed in approximately 20% of the cases. The duration of beating activity varied from several seconds to tens of minutes. In the presence of low concentrations (1 microM) of 5-HT, both the probability of mode transitions and the duration of induced beating activity increased significantly. 3. These results indicate that at least two stable modes of electrical activity can coexist in R15 neurons and that this bistability can be regulated by 5-HT. In general, these conclusions agree with the results from analyses of mathematical models of R15. Although the function of these dynamic properties in R15 is speculative, our results, interpreted on the background of the model, support the notion that nonlinear dynamical properties of individual neurons can endow them with richer forms of information processing than has generally been appreciated.

Amino Acid Sequence↗

PubMed2000

Accurate predictive modeling of response variables under dynamic condition without the use of past response data

One promising attribute of the dynamic predictive modeling method introduced by Rollins et al. [D.K. Rollins, J. Liang, P. Smith, Accurate simplistic predictive modeling of nonlinear dynamic processes, ISA Transactions 37(4) (1998) 193-203] is its ability to accurately predict output response without the use of online output data. The proposed method only needs online input data to accurately predict output behavior once the semi-empirical model has been identified using offline data. This ability is critical to chemical processes because many output variables (such as chemical composition) are often measured infrequently, inaccurately, or not at all. In addition, in the presence of extremely high measurement noise of the output variable, this work will demonstrate very accurate predictive performance. Finally, this article will show that the method of Rollins et al. can predict better without the use of output data than with the use of output data in the case of large measurement variance. Thus, the proposed method is being recommended for its accuracy, especially in situations where online output response data is limited or inaccurate.

Journal Article↗

PubMed1992

A parameter optimization approach for the optimal control of large-scale musculoskeletal systems.

This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).

Adult↗

PubMed2005

Path-dependent economic evolution with capital accumulation and education.

This paper proposes a dynamic economic model with wealth accumulation and human capital accumulation. The economic system consists of one production sector and one university. The university carries out education. The model describes a dynamic interdependence between wealth accumulation, human capital accumulation, and division of labor under perfect economic competition and the government intervention in education. We provide conditions for the existence of equilibrium points and stability of the nonlinear dynamic system. The simulation results demonstrate path-dependent processes of the nonlinear evolution. Some insights into East Asia's industrializing processes are provided.

Journal Article↗

PubMed2002

Stochastic analysis of a non-normal dynamical system mimicking a laminar-to-turbulent subcritical transition.

The effects of stochastic perturbations on a non-normal dynamical system mimicking a laminar-to-turbulent subcritical transition are investigated both analytically and numerically. It is found that a nonlinear dynamical system with non-normal transient linear growth is very sensitive to the presence of weak random perturbations. The effect of non-normality on the exit probability from the zero fixed point is analyzed numerically for small values of the noise intensity parameter. It is found that an increase in the intensity of the noise, or a decrease of the non-normality parameter leads to qualitative changes in the behavior of the trajectories that can be interpreted as noise-induced phase transitions. By using the Itô formula and the adiabatic elimination procedure a stochastic equation governing the slow evolution of the energy of the non-normal system is derived.

Journal Article↗

PubMed2006

Fully nonlinear evolution of a cylindrical vortex sheet in incompressible Richtmyer-Meshkov instability.

Fully nonlinear motion of a circular interface in incompressible Richtmyer-Meshkov instability is investigated by treating it as a nonuniform vortex sheet between two different fluids. There are many features in cylindrical geometry such as the existence of two independent spatial scales, radius and wavelength, and the ingoing and outgoing growth of bubbles and spikes. Geometrical complexities lead to the results that nonlinear dynamics of the vortex sheet is determined from the inward and outward motion rather than bubbles and spikes, and that the nonlinear growth strongly depends on mode number.

Journal Article↗

PubMed2003

Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling.

Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Paget's disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget's disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Paget's disease.

Autocrine Communication↗

PubMedDate not supplied

Fractals in physiology and medicine.

Nonlinear dynamics, a branch of the basic sciences that studies complex physical systems, offers novel approaches to long-standing problems of physiological form and function. The nonlinear concept of fractals, introduced and developed over the last decade, provides insights into the organization of complex structures such as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.

Algorithms↗

PubMed2006

Feedback control of subcritical oscillatory instabilities.

Feedback control of a subcritical oscillatory instability is investigated in the framework of a globally-controlled complex Ginzburg-Landau equation that describes the nonlinear dynamics near the instability threshold. The control is based on a feedback loop between the system linear growth rate and the maximum of the amplitude of the emerging pattern. It is shown that such control can suppress the blow up and result in the formation of spatially localized pulses similar to oscillons. In the one-dimensional case, depending on the values of the linear and nonlinear dispersion coefficients, several types of the pulse dynamics are possible in which the computational domain contains: (i) a single stationary pulse; (ii) several coexisting stationary pulses; (iii) competing pulses that appear one after another at random locations so that at each moment of time there is only one pulse in the domain; (iv) spatiotemporally chaotic system of short pulses; (v) spatially-synchronized pulses. Similar dynamic behavior is found also in the two-dimensional case. The effect of the feedback delay is also studied. It is shown that the increase of the delay leads to an oscillatory instability of the pulses and the formation of pulses with oscillating amplitude.

Journal Article↗

PubMed2006

Effect of conjugation path length on quadratic nonlinear optical properties of monomer and aggregates of zwitterionic merocyanine dyes.

We present a quantum-chemical analysis of the conjugation path length effect on first hyperpolarizabilities of a series of zwitterionic merocyanine dyes whose synthesis has been reported earlier (J. Am. Chem. Soc.2002, 124, 9431, J. Am. Chem. Soc. 1997, 119, 3144). The effect of the conjugation path lengths is evaluated to demonstrate the engineering guidelines for enhancing molecular optical nonlinearity. The first hyperpolarizabilities are calculated for extended conjugated monomer and H and J type aggregates of merocyanine dyes, to provide insight into the intermolecular interactions and the relationship between structural and collective nonlinear optical properties. The molecular geometries for monomers are obtained via B3LYP/6-31G(d,p) level optimization including the SCRF/PCM approach, and the dynamic nonlinear optical (NLO) properties for monomer and aggregates are calculated with the ZINDO/CV method, including solvent effects. It is found that the chain length dependence of the first nonlinearity peaks at n = 6 and then it starts changing slowly for monomer and aggregates of zwitterionic merocyanine dyes. It is concluded that an excellent NLO response in solution might vanish when the active chromophore forms higher H aggregates. The importance of our results on the design of electrooptic materials has been discussed.

Journal Article↗

PubMed2006

Fast thermo-optical excitability in a two-dimensional photonic crystal.

We experimentally demonstrate excitability in a semiconductor two-dimensional photonic crystal. Excitability is a nonlinear dynamical mechanism underlying pulselike responses to small perturbations in systems possessing one stable state. We show that a band-edge photonic crystal resonator exhibits class II excitability, resulting from the nonlinear coupling between the high-Q optical mode, the charge-carrier density, and the fast (sub-micros) thermal dynamics. In this context, the critical slowing down of the electro-optical dynamics close to the excitable threshold can delay the optical response by an amount comparable to the duration of the output pulse (5 ns). The latter results from a short thermal dynamical excursion along a high local intensity manifold of the phase space.

Arsenicals↗

PubMed2004

Entropy of dialogues creates coherent structures in e-mail traffic.

We study the dynamic network of e-mail traffic and find that it develops self-organized coherent structures similar to those appearing in many nonlinear dynamic systems. Such structures are uncovered by a general information theoretic approach to dynamic networks based on the analysis of synchronization among trios of users. In the e-mail network, coherent structures arise from temporal correlations when users act in a synchronized manner. These temporally linked structures turn out to be functional, goal-oriented aggregates that must react in real time to changing objectives and challenges (e.g., committees at a university). In contrast, static structures turn out to be related to organizational units (e.g., departments).

Journal Article↗