Use Of Dynamical Systems Theory Research Articles

The Wire Is Not the Territory: Understanding Representational Drift in Olfaction With Dynamical Systems Theory.

Representational drift is a phenomenon of increasing interest in the cognitive and neural sciences. While investigations are ongoing for other sensory cortices, recent research has demonstrated the pervasiveness in which it occurs in the piriform cortex for olfaction. This gradual weakening and shifting of stimulus-responsive cells has critical implications for sensory stimulus-response models and perceptual decision-making. While representational drift may complicate traditional sensory processing models, it could be seen as an advantage in olfaction, as animals live in environments with constantly changing and unpredictable chemical information. Non-topographical encoding in the olfactory system may aid in contextualizing reactions to promiscuous odor stimuli, facilitating adaptive animal behavior and survival. This article suggests that traditional models of stimulus-(neural) response mapping in olfaction may need to be reevaluated and instead motivates the use of dynamical systems theory as a methodology and conceptual framework.

Furthering the discussion on the use of dynamical systems theory for investigating resilience in sport.

Furthering the discussion on the use of dynamical systems theory for investigating resilience in sport.

Older women and sexuality: Narratives of gender, age, and living environment

ABSTRACTLittle research has explored the intersection of aging and sexuality. This qualitative study is informed by a life course approach and narrative gerontology methods. Semistructured interviews were conducted with 13 women age 55 and older to explore the effects of gender, aging, and living environment on past and current sexual experiences. Subthemes from each major theme are discussed, including: (a) messages about and perceived effects of gender, (b) perceived effects of aging, and (c) perceived effects of living environment. Findings support the use of dynamical systems theory to study women’s sexual experiences.

The rate of convergence to early asymptotic behaviour in age-structured epidemic models

Age structure is incorporated in many types of epidemic models. Often it is convenient to assume that such models converge to early asymptotic behaviour quickly, before the susceptible population has been appreciably depleted. We make use of dynamical systems theory to show that for some reasonable parameter values, this convergence can be slow. Such a possibility should therefore be considered when parametrising age-structured epidemic models.

Oscillations toward the Singularity of Locally Rotationally Symmetric Bianchi Type IX Cosmological Models with Vlasov Matter

We analyze the dynamics of a class of cosmological solutions of the Einstein–Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively through Einstein's equations of general relativity. The cosmological models we consider are spatially homogeneous, of Bianchi type IX, and locally rotationally symmetric (LRS). We prove that generic solutions exhibit an oscillatory behavior close to the singularities (the “big bang” in the past and the “big crunch” in the future); this is in contrast to the behavior of Einstein-vacuum or Einstein–Euler solutions. To establish this result we make use of dynamical systems theory; we introduce dimensionless dynamical variables that are defined on a compact state space. In this formulation the oscillatory behavior of generic solutions is represented by the existence of heteroclinic cycles on the boundary of the state space.

New trends in localization theory

In this article we discuss some recent trends in the research of electron and phonon localization, specially in the field of quasiperiodic potentials. Then, a new scheme to detect and classify localization is developed by studying the band scaling of a related supercrystal made from replicas of the system. For one dimension, this leads to the use of dynamical systems theory to obtain the localization length and the scaling exponents of the wave functions.

Questions For The Dynamicist: The Use of Dynamical Systems Theory in the Philosophy of Cognition

The concepts and powerful mathematical tools of Dynamical Systems Theory (DST) yield illuminating methods of studying cognitive processes, and are even claimed by some to enable us to bridge the notorious explanatory gap separating mind and matter. This article includes an analysis of some of the conceptual and empirical progress Dynamical Systems Theory is claimed to accomodate. While sympathetic to the dynamicist program in principle, this article will attempt to formulate a series of problems the proponents of the approach in question will need to face if they wish to prolong their optimism. The main points to be addressed involve the reductive tendencies inherent in Dynamical Systems Theory, its somewhat muddled position relative to connectionism, the metaphorical nature DST-C exhibits which hinders its explanatory potential, and DST-C's problematic account of causality. Brief discussions of the mathematical and philosophical backgrounds of DST, seminal experimental work and possible adaptations of the theory or alternative suggestions (dynamicist connectionism, neurophenomenology, R&D theory) are included.

Discretization of implicit ODEs for singular root-finding problems

This paper addresses the use of dynamical system theory to tackle singular root-finding problems. The use of continuous-time methods leads to implicit differential systems when applied to singular nonlinear equations. The analysis is based on a taxonomy of singularities and uses previous stability results proved in the context of quasilinear implicit ODEs. The proposed approach provides a framework for the systematic formulation of quadratically convergent iterations to singular roots. The scope of the work includes also the introduction of discrete-time analysis techniques for singular problems which are based on continuous-time stability and numerical stability. Some numerical experiments illustrate the applicability of the proposed techniques.

Coordinates transformation and learning control for visually-guided voluntary movement with iteration: A Newton-like method in a function space

In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n + 1)-th iteration is a sum of the motor command in the n-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in the n-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes.