Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201

Cognitive stories and the image of mathematics

This paper considers two models of embodied mathematical cognition (a modular model and a dynamic model), and analyses the image of mathematics that they support.; Este artículo considera dos modelos de cognición matemática corporizada (un modelo modular y un modelo dinámico), y analiza la imagen de las matemáticas que apoya

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Cognitive stories and the image of mathematics

This paper considers two models of embodied mathematical cognition (a modular model and a dynamic model), and analyses the image of mathematics that they support.; Este artículo considera dos modelos de cognición matemática corporizada (un modelo modular y un modelo dinámico), y analiza la imagen de las matemáticas que apoya

Complex Dynamics in Dedicated / Multifunctional Neural Networks and Chaotic Nonlinear Systems

We study complex behaviors arising in neuroscience and other nonlinear systems by combining dynamical systems analysis with modern computational approaches including GPU parallelization and unsupervised machine learning. To gain insights into the behaviors of brain networks and complex central pattern generators (CPGs), it is important to understand the dynamical principles regulating individual neurons as well as the basic structural and functional building blocks of neural networks. In the first section, we discuss how symbolic methods can help us analyze neural dynamics such as bursting, tonic spiking and chaotic mixed-mode oscillations in various models of individual neurons, the bifurcations that underlie transitions between activity types, as well as emergent network phenomena through synergistic interactions seen in realistic neural circuits, such as network bursting from non-intrinsic bursters. The second section is focused on the origin and coexistence of multistable rhythms in oscillatory neural networks of inhibitory coupled cells. We discuss how network connectivity and intrinsic properties of the cells affect the dynamics, and how even simple circuits can exhibit a variety of mono/multi-stable rhythms including pacemakers, half-center oscillators, multiple traveling-waves, fully synchronous states, as well as various chimeras. Our analyses can help generate verifiable hypotheses for neurophysiological experiments on central pattern generators. In the last section, we demonstrate the inter-disciplinary nature of this research through the applications of these techniques to identify the universal principles governing both simple and complex dynamics, and chaotic structure in diverse nonlinear systems. Using a classical example from nonlinear laser optics, we elaborate on the multiplicity and self-similarity of key organizing structures in 2D parameter space such as homoclinic and heteroclinic bifurcation curves, Bykov T-point spirals, and inclination flips. This is followed by detailed computational reconstructions of the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas). The generality of our modeling approaches could lead to novel methodologies and nonlinear science applications in biological, medical and engineering systems

Numerical representations of fluid mixing

The work contained within this thesis is concerned with a theoretical investigatiop of both laminar and thermally driven types of cavity flow, together with an analysis of their associated mixing processes which find applications to Industrial mixing and also to the environment. The mixing efficiency has been viewed from two perspectives namely the tracking of a selection of fluid particles, and also the simulation of the dispersive mixing of a coloured fluid element as carried along by the flow. This thesis also incorporates features of both Newtonian and a wide range of non-Newtonian fluids

Transdisciplinary Creative Ecologies in Contemporary Art within Emergent Processes

This research is composing in the moving with affective speeds and rhythms, instead of unfolding direct and in linear ways. It is important to come across different planes of composition in movement. There are so many planes of voices spinning around in relation. Research-creation seems as forms of relations and an invitation to appreciate the collectivity at the heart of thinking. The many entering-into relation within a differential thought in the making of its own. Emergent properties in non-human interactions, such as those presented in Steven Shaviro ́s Against Self-Organization (2009) and Brain Massumi, are symptomatic of how individualities relate to creative tendencies in relation to the human, non-human dynamism, and emergence as a state or condition. Emergence can be co-joined around the notion of self-organization, “the spontaneous production of a level of reality having its own rules of formation and order of connection” (Massumi, 2002). Self-organization emphasizes on matter-energy which Gilles Deleuze conceives of as the difference or line variation running through all things. Therefore, Deleuze focuses on immanence, how new forms are created, and on the ways in which material bodyings self-organize rather than being forced to do so. Moreover, the research in this dissertation seeks to generate a charged environment where human and non-human emergent processes activate creative encounters that co-create and co-shape each other (Delueze and Guattari, 2003; Stangers, 2017; Manning 2009). This study investigates how complexities and relations expand as an attractor of potentialities, that informs a matrix as movement, and recognizes nodes of the matrix as connections for such movements. My research is transdisciplinary, where experimental work interconnects art, science- zoology, architecture and process philosophy, and conjoins such with non-human emergent processes which are complex systems that activate intermodalities in their doing. These areas of research focus on, thread processes and transdisciplinary art doings.Textiles seen as intensities, transformations, movements, multiplicities of sensations experienced by familiar bodies in resonance with the world in acts of co-composing

Homoclinic puzzles and chaos in a nonlinear laser model

We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using MatCont and a newly developed technique called the Deterministic Chaos Prospector (DCP) utilizing symbolic dynamics on fast parallel computing hardware with graphics processing units (GPUs), we exhibit how specific codimension-two bifurcations originate and pattern regions of chaotic and simple dynamics in this classical model. We show detailed computational reconstructions of key bifurcation structures such as Bykov T-point spirals and inclination flips in 2D parameter space, as well as the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas).Comment: 28 pages, 23 figure