Dynamical Systems


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Dynamical Systems

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 nonlinear dynamical systems.

Dynamical Systems

A series of equations in which the output of one becomes the input of another. One equation may determine a company's earnings for a particular period. The earnings, then, may be put into another equation to determine the earnings per share. This is a simple example of dynamical systems. It may (and often does) include a long string of equations.
References in periodicals archive ?
These issues and the methods to resolve them are of great importance also for other models in cellular biology and also for slow-fast dynamical systems in general.
Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems' trajectories "are tightly constrained to follow algebraic laws," said McMullen.
Rare dangerous or useful attractors may find application in the pendulum-like dynamical systems.
Using the normal probability distribution assumptions we can derive the Gaussian white noise intensity value, respectively value of combined dynamical systems stochastic part.
Remark that the trajectories of the preceding conservative (potential or nonpotential) dynamical systems divides into three classes:
Connecting orbits are very important in the global study of dynamical systems, acting as separatrices of solutions in the phase portrait, giving a better understanding of the behavior of nearby solutions.
Section 2 provides the necessary background information on the invariance and conserved quantities of dynamical system and especially the Noether's theorem.
This equivalence is used to suggest a class of resolvent dynamical systems for the quasi variational inclusions (2.
These workshops, which were attended by more than eighty scientists from twenty three countries, focused on difference equations and their interactions with orthogonal polynomials and hypergeometric functions (with special emphasis on operator equations and factorization, and Fourier expansions), difference and differential equations and their interactions with chaos and dynamical systems as well as their applications in Mathematical Physics (q-harmonic oscillators, discrete and continuous Schrodinger operators, Emden-Fowler dynamic equations) and Numerical Analysis (difference schemes for quasi-linear evolution problems).
Moreover, one of the hallmarks of dynamical systems and chaos theory is the concept of sensitivity to initial conditions.
In short, complex dynamical systems are self-patterning, self-regulating and commonly surprising.
John Doyle, a professor of control and dynamical systems at the California Institute of Technology, has likened the complexity of a biological system to that of a Boeing 777 jet.

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