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In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems .
A state diagram for a simple example is shown in the figure on the right, using a directed graph to picture the state transitions. The states represent whether a hypothetical stock market is exhibiting a bull market, bear market, or stagnant market trend during a given week. According to the figure, a bull week is followed by another bull week ...
Continuous optimization is a branch of optimization in applied mathematics. [1] As opposed to discrete optimization, the variables used in the objective function are required to be continuous variables—that is, to be chosen from a set of real values between which there are no gaps (values from intervals of the real line).
Markov chains and continuous-time Markov processes are useful in chemistry when physical systems closely approximate the Markov property. For example, imagine a large number n of molecules in solution in state A, each of which can undergo a chemical reaction to state B with a certain average rate. Perhaps the molecule is an enzyme, and the ...
Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits per symbol, as measured by the rate R, that should be communicated over a channel, so that the source (input signal) can be approximately reconstructed at the receiver (output signal) without ...
Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a ...
A (real-world) dynamic system may be continuous or discrete. Continuous dynamic systems (like physical systems with material objects moving in space) are characterized by state variables the values of which change continuously, while the state variable values of discrete dynamic systems (like predator-prey ecosystems) "jump", that is, they are ...