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In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
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Alan David Sokal is an American professor of mathematics at University College London and professor emeritus of physics at New York University. He works in statistical mechanics and combinatorics. He is a critic of postmodernism, and caused the Sokal affair in 1996 when his deliberately nonsensical paper was published by Duke University Press's Social Text. He also co-authored a paper criticizing the critical positivity ratio concept in positive psychology.
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The Ramsey–Cass–Koopmans model, or Ramsey growth model, is a neoclassical model of economic growth based primarily on the work of Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans. The Ramsey–Cass–Koopmans model differs from the Solow–Swan model in that the choice of consumption is explicitly microfounded at a point in time and so endogenizes the savings rate. As a result, unlike in the Solow–Swan model, the saving rate may not be constant along the transition to the long run steady state. Another implication of the model is that the outcome is Pareto optimal or Pareto efficient.
The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. In popular media the "butterfly effect" stems from the real-world implications of the Lorenz attractor, namely that several different initial chaotic conditions evolve in phase space in a way that never repeats, so all chaos is unpredictable. This underscores that chaotic systems can be completely deterministic and yet still be inherently unpredictable over long periods of time. Because chaos continually increases in systems, we cannot predict the future of systems well. E.g., even the small flap of a butterfly’s wings could set the world on a vastly different trajectory, such as by causing a hurricane. The shape of the Lorenz attractor itself, when plotted in phase space, may also be seen to resemble a butterfly.
Barbara Lee Fredrickson is an American professor in the department of psychology at the University of North Carolina at Chapel Hill, where she is the Kenan Distinguished Professor of Psychology. She is also the Principal Investigator of the Positive Emotions and Psychophysiology Lab (PEPLab) at the University of North Carolina at Chapel Hill.
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Marcial Losada (1939–2020) was a Chilean psychologist, consultant, and former director of the Center for Advanced Research (CFAR) in Ann Arbor, Michigan. He is known for his work in academia and business focusing on the development of "high performance teams", and having participated in partially retracted collaborative work with Barbara Fredrickson of the University of North Carolina, a retraction for which he has been assigned the culpability.
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Undulatory locomotion is the type of motion characterized by wave-like movement patterns that act to propel an animal forward. Examples of this type of gait include crawling in snakes, or swimming in the lamprey. Although this is typically the type of gait utilized by limbless animals, some creatures with limbs, such as the salamander, forgo use of their legs in certain environments and exhibit undulatory locomotion. In robotics this movement strategy is studied in order to create novel robotic devices capable of traversing a variety of environments.
In mathematics, a strange nonchaotic attractor (SNA) is a form of attractor which, while converging to a limit, is strange, because it is not piecewise differentiable, and also non-chaotic, in that its Lyapunov exponents are non-positive. SNAs were introduced as a topic of study by Grebogi et al. in 1984. SNAs can be distinguished from periodic, quasiperiodic and chaotic attractors using the 0-1 test for chaos.
References
- 1 2 Losada, M. and Heaphy, E. (2004). "The role of positivity and connectivity in the performance of business teams: A nonlinear dynamics model", American Behavioral Scientist, 47 (6), pp. 740–765.
- ↑ "Ratio for a good life exposed as 'nonsense'". Science News . 12 August 2013. Archived from the original on 26 August 2013. Retrieved 15 August 2013.
- Brown, N. J. L., Sokal, A. D., & Friedman, H. L. (2013). "The complex dynamics of wishful thinking: the critical positivity ratio", American Psychologist, 68 (9), pp. 801-813 - ↑ Navas, A. (2011), "Un cas d'inconscience (?)", Images des Mathématiques(in French)
