Concept explainers
To calculate: The value of the equilibria of discrete time dynamical system
Answer to Problem 34E
The value of the equilibria of discrete time dynamical system
Explanation of Solution
Given information:
The discrete time dynamical system,
Formula used:
The steps to evaluate the equilibrium of discrete time dynamical system are as follows:
1. For discrete time dynamical system,
2. With help of subtraction transfer all the term on left hand side and keep 0 on right hand side.
3. Factorize the expression so obtained.
4. Equate each factor to 0.
5. Interpret the results obtained.
Calculation:
Consider the provided discrete time dynamical system,
Recall the steps to evaluate the equilibrium of discrete time dynamical system are as follows:
1. For discrete time dynamical system,
2. With help of subtraction transfer all the term on left hand side and keep 0 on right hand side.
3. Factorize the expression so obtained.
4. Equate each factor to 0.
5. Interpret the results obtained.
Replace
Multiply both sides by the denominator
Subtract the term
Factor out the term
Equate each term to zero.
Either
Simplify the terms obtained above.
Add K on both the sides also add 1 on both the sides,
Therefore, either
Therefore, equilibrium points are
If
If
Thus, the value of the equilibria of discrete time dynamical system
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