Question

What is Steady state and un steady state models? Explain it with suitable example.

Answer 1

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time.[1] In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:

{\displaystyle {\frac {\partial p}{\partial t}}=0\quad {\text{for all }}t.} {\displaystyle {\frac {\partial p}{\partial t}}=0\quad {\text{for all }}t.}

In discrete time, it means that the first difference of each property is zero and remains so:

{\displaystyle p_{t}-p_{t-1}=0\quad {\text{for all }}t.} {\displaystyle p_{t}-p_{t-1}=0\quad {\text{for all }}t.}

The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future.[1] In stochastic systems, the probabilities that various states will be repeated will remain constant. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state.