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The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior . The Duffing map takes a point ( x n , y n ) in the plane and maps it to a new point given by
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.
Spiral Dynamics describes how value systems and worldviews emerge from the interaction of "life conditions" and the mind's capacities. [8] The emphasis on life conditions as essential to the progression through value systems is unusual among similar theories, and leads to the view that no level is inherently positive or negative, but rather is a response to the local environment, social ...
In psychology, temporal motivation theory (TMT) is an integrative motivational theory developed by Piers Steel and Cornelius J. König. The theory emphasizes time as a critical and motivational factor. The argument for a broad, integrative theory stems from the absence of a single theory that can address motivation in its entirety.
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]
Such systems can experience bifurcation (a qualitative change in behavior) as a function of its bifurcation parameters and often exhibit chaos. [2] Dynamical neuroscience describes the non-linear dynamics at many levels of the brain from single neural cells [3] to cognitive processes, sleep states and the behavior of neurons in large-scale ...
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.