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Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
A real dynamical system, real-time dynamical system, continuous time dynamical system, or flow is a tuple (T, M, Φ) with T an open interval in the real numbers R, M a manifold locally diffeomorphic to a Banach space, and Φ a continuous function. If Φ is continuously differentiable we say the system is a differentiable dynamical system.
Dynamicism, also termed dynamic hypothesis or dynamic cognition, is an approach in cognitive science popularized by the work of philosopher Tim van Gelder. [1] [2] It argues that differential equations and dynamical systems are more suited to modeling cognition rather than the commonly used ideas of symbolicism, connectionism, or traditional computer models.
System dynamics is an aspect of systems theory as a method to understand the dynamic behavior of complex systems. The basis of the method is the recognition that the structure of any system, the many circular, interlocking, sometimes time-delayed relationships among its components, is often just as important in determining its behavior as the ...
A cornerstone of EDM is recognition that time series observed from a dynamical system can be transformed into higher-dimensional state-spaces by time-delay embedding with Takens's theorem. The state-space models are evaluated based on in-sample fidelity to observations, conventionally with Pearson correlation between predictions and observations.
According to psychologist Ruth Kanfer, motives are stable dispositional tendencies that contrast with the dynamic nature of motivation as a fluctuating internal state. [12] Motivation is closely related to ability, effort, and action. [32] An ability is a power to perform an action, like the ability to walk or to write.
Dynamic decision making research uses computer simulations which are laboratory analogues for real-life situations. These computer simulations are also called “microworlds” [4] and are used to examine people's behavior in simulated real world settings where people typically try to control a complex system where later decisions are affected by earlier decisions. [5]
Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on the case of algebraic dynamics, where a polynomial or rational function is iterated. In geometric terms, that amounts to iterating a mapping from some algebraic variety to itself.