Terminology for the Description of Dynamics (TEDDY) aims to provide an ontology for dynamical behaviours, observable dynamical phenomena, and control elements of bio-models and biological systems in Systems Biology and Synthetic Biology. [1] [2]
Terminology for the Description of Dynamics (TEDDY) aims to provide an ontology for dynamical behaviours, observable dynamical phenomena, and control elements of bio-models and biological systems in Systems Biology and Synthetic Biology. [1] [2]
Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. "Chaos" is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals, self-organization, and reliance on programming at the initial point known as sensitive dependence on initial conditions. The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, e.g. a butterfly flapping its wings in Brazil can cause a hurricane in Texas.
Control theory in control systems engineering is a subfield of mathematics that deals with the control of continuously operating dynamical systems in engineered processes and machines. The objective is to develop a control model for controlling such systems using a control action in an optimum manner without delay or overshoot and ensuring control stability.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world.
Molecular dynamics (MD) is a computer simulation method for studying the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic evolution of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanics force fields. The method was originally developed within the field of theoretical physics in the late 1950s but is applied today mostly in chemical physics, materials science and the modelling of biomolecules.
Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them. Example scenarios are ageing populations, population growth, or population decline.
Systems science is an interdisciplinary field that studies the nature of systems—from simple to complex—in nature, society, cognition, engineering, technology and science itself. To systems scientists, the world can be understood as a system of systems. The field aims to develop interdisciplinary foundations that are applicable in a variety of areas, such as psychology, biology, medicine, communication, business management, engineering, and social sciences.
Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
A metapopulation consists of a group of spatially separated populations of the same species which interact at some level. The term metapopulation was coined by Richard Levins in 1969 to describe a model of population dynamics of insect pests in agricultural fields, but the idea has been most broadly applied to species in naturally or artificially fragmented habitats. In Levins' own words, it consists of "a population of populations".
A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t. This may be done synchronously or asynchronously.
Adilson E. Motter, is the Charles E. and Emma H. Morrison Professor of Physics at Northwestern University, where he has helped develop the concept of synthetic rescue in network biology as well as methods to control the nonlinear dynamics of complex networks. In joint work with Takashi Nishikawa, he discovered the phenomenon of asymmetry-induced symmetry. Motter's research is focused on complex systems and nonlinear phenomena, primarily involving complex networks, systems biology, chaos and statistical physics.
N-body units are a completely self-contained system of units used for N-body simulations of self-gravitating systems in astrophysics. In this system, the base physical units are chosen so that the total mass, M, the gravitational constant, G, and the virial radius, R, are normalized. The underlying assumption is that the system of N objects (stars) satisfies the virial theorem. The consequence of standard N-body units is that the velocity dispersion of the system, v, is and that the dynamical or crossing time, t, is . The use of standard N-body units was advocated by Michel Hénon in 1971. Early adopters of this system of units included H. Cohn in 1979 and D. Heggie and R. Mathieu in 1986. At the conference MODEST14 in 2014, D. Heggie proposed that the community abandon the name "N-body units" and replace it with the name "Hénon units" to commemorate the originator.
Valentin Afraimovich was a Soviet, Russian and Mexican mathematician. He made contributions to dynamical systems theory, qualitative theory of ordinary differential equations, bifurcation theory, concept of attractor, strange attractors, space-time chaos, mathematical models of nonequilibrium media and biological systems, traveling waves in lattices, complexity of orbits and dimension-like characteristics in dynamical systems.
The dynamical systems approach to neuroscience is a branch of mathematical biology that utilizes nonlinear dynamics to understand and model the nervous system and its functions. In a dynamical system, all possible states are expressed by a phase space. Such systems can experience bifurcation as a function of its bifurcation parameters and often exhibit chaos. Dynamical neuroscience describes the non-linear dynamics at many levels of the brain from single neural cells to cognitive processes, sleep states and the behavior of neurons in large-scale neuronal simulation.
Biological applications of bifurcation theory provide a framework for understanding the behavior of biological networks modeled as dynamical systems. In the context of a biological system, bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the behavior of the system. The ability to make dramatic change in system output is often essential to organism function, and bifurcations are therefore ubiquitous in biological networks such as the switches of the cell cycle.
In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer order. Such systems are said to have fractional dynamics. Derivatives and integrals of fractional orders are used to describe objects that can be characterized by power-law nonlocality, power-law long-range dependence or fractal properties. Fractional-order systems are useful in studying the anomalous behavior of dynamical systems in physics, electrochemistry, biology, viscoelasticity and chaotic systems.
Edward Ott is an American physicist most noted for his contributions to the development of chaos theory.
David S. Broomhead was a British mathematician specialising in dynamical systems and was professor of applied mathematics at the School of Mathematics, University of Manchester.
Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905 Einstein argued that the requirement of consistency between thermodynamics and electromagnetism leads to the conclusion that light is quantized obtaining the relation . This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules. Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition there is a quest for the theory to be relevant for a single individual quantum system.
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