Examples of using Dynamical system in English and their translations into Vietnamese
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Tochastic processes(random dynamical systems).
Thus, the resulting dynamical system is a Hamiltonian system of the form.
A Lyapunov function for an autonomous dynamical system.
The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state.
A Lyapunov candidate-function for an autonomous dynamical system.
Reconnection of equations will yield a set of equations called the dynamical system which includes thousands, hundreds of thousands, or millions of data points.
The dynamical system concept is a mathematical formalization for any fixed"rule" that describes the time dependence of a point's position in its ambient space.
In control theory atrajectory is a time-ordered set of states of a dynamical system(see e.g. Poincaré map).
Qualitative behavior of dynamical systems or equations of motions that are primarily mechanical can impact solutions of differential equation".
A general way to establish Lyapunov stability orasymptotic stability of a dynamical system is by means of Lyapunov functions.
Chaos theory says that complex dynamical systems become unstable because of disturbances in their environments after which a strange attractor draws the trajectory of the stress.”.
Lyapunov contributed to several fields, including differential equations,potential theory, dynamical systems and probability theory.
Artists know that like the sensitivity of a chaotic dynamical system, a change on small part of a painting or poem may destroy or transform the work.".
Here the necessary conditions are shown for minimization of a functional. Take x{\displaystyle x}to be the state of the dynamical system with input u{\displaystyle u}, such that.
In contrast, for a feedback apparatus used to control a dynamical system, the objective is to give the closed-loop system improved response as compared to the uncompensated system. .
By the chain rule, for any function, H: R n→ R{\displaystyle H:\mathbb{R}^{n}\to\mathbb{R}}, the time derivative of thefunction evaluated along a solution of the dynamical system is.
Lyapunov is known for his development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory.
Unobservable poles are not present in the transfer function realization of a state-space representation,which is why sometimes the latter is preferred in dynamical systems analysis.
Interactions between neurons firing in the brain are also an example of a dynamical system- albeit one that's especially subtle and hard to pin down in a definable list of rules.
What if we could just turn off that brain for the brief amount of time until the seizure dies away,and cause the brain to be restored to its initial state, like a dynamical system that's being coaxed down into a stable state?
Many parts of the qualitative theory of differential equations and dynamical systems deal with asymptotic properties of solutions and the trajectories- what happens with the system after a long period of time.
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic,topology and its interactions with algebra, and dynamical systems.
At any given time, a dynamical system has a state given by a tuple of real numbers(a vector) that can be represented by a point in an appropriate state space(a geometrical manifold).
What if we could just turn off that brain for a brief amount of time, until the seizure dies away, and cause the brain to be restored to its initial state--sort of like a dynamical system that's being coaxed down into a stable state.
In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space.
In control theory and stability theory, the Nyquist stability criterion, discovered by Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932,is a graphical technique for determining the stability of a dynamical system.
According to Wikipedia,“The Lorenz attractor, introduced by Edward Lorenz in 1963,is a non-linear three-dimensional deterministic dynamical system derived from the simplified equations of convection rolls arising in the dynamical equations of the atmosphere.
DeMarco then went off todo pioneering work applying techniques from dynamical systems to questions in number theory, for which she will receive the Satter Prize- awarded to a leading female researcher- from the American Mathematical Society on January 5.