Linear operators form the backbone of modern mathematical analysis and have become indispensable in characterising the behaviour of dynamical systems. At their core, these operators are functions that ...

Intrinsic neural attractors and extrinsic environmental inputs jointly steer the dynamic trajectories of brain activity ...

Engineers have demonstrated a simple computational approach for supporting the classification performance of neural networks operating on sensor time series. The proposed technique involves feeding ...

SIAM Journal on Numerical Analysis, Vol. 14, No. 2 (Apr., 1977), pp. 180-193 (14 pages) Kalman [9] introduced a method for estimating the state of a discrete linear dynamic system subject to noise.

Epilepsy is a disorder characterized by paroxysmal transitions between multistable states. Dynamical systems have been useful for modeling the paroxysmal nature of seizures. At the same time, ...

Unified treatment of continuous and discrete time systems from a state-variable viewpoint; emphasis on linear systems. Concept of state, writing and solving state equations, controllability and ...

A system of equations where the output of one equation is part of the input for another. A simple version of a dynamical system is linear simultaneous equations. Non-linear simultaneous equations are ...

We often encounter nonlinear dynamical systems that behave unpredictably, such as the earth's climate and the stock market. To analyze them, measurements taken over time are used to reconstruct the ...