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Field theory is centered around the idea that a person's life space determines their behavior. [2] Thus, the equation was also expressed as B = f(L), where L is the life space. [4] In Lewin's book, he first presents the equation as B = f(S), where behavior is a function of the whole situation (S). [5]
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
The set of possible combinations of state variable values is called the state space of the system. The equations relating the current state of a system to its most recent input and past states are called the state equations, and the equations expressing the values of the output variables in terms of the state variables and inputs are called the ...
A state-space model is a representation of a system in which the effect of all "prior" input values is contained by a state vector. In the case of an m-d system, each dimension has a state vector that contains the effect of prior inputs relative to that dimension. The collection of all such dimensional state vectors at a point constitutes the ...
The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map , x n + 1 = r x n ( 1 − x n ) {\displaystyle x_{n+1}=rx_{n}(1-x_{n})} , whose basins of attraction for various values of the parameter r {\displaystyle r} are shown ...
For example, if the dimension of the state space is greater than the dimension of the output, then there will be a set of possible state configurations for each individual output. That is, the system can have significant zero dynamics , which are trajectories of the system that are not observable from the output.
Furthermore, the interaction of the person (P), and the environment (E) produces this life space. In symbolic expression, B=ƒ(LS)=F(P,E). [6] An example of a more complex life-space concept is the idea that two people's experience of a situation can become one when they converse together.
State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with the desired property. Problems are often modelled as a state space, a set of states that a problem