Linear Algebra - Equilibrium state of dynamical system

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SUMMARY

The discussion focuses on finding the equilibrium state of a dynamical system represented by the equations x1(t+1) = -0.5x1(t) - 0.2x2(t) - 1 and x2(t+1) = 26x1(t) + 0.7x2(t) + 1. To determine the equilibrium state, one must recognize that at equilibrium, x1(t+1) equals x1(t) and x2(t+1) equals x2(t). This understanding is crucial for solving the system of equations.

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  • Understanding of dynamical systems
  • Familiarity with equilibrium concepts in mathematics
  • Basic knowledge of solving linear equations
  • Experience with subscripts in mathematical notation
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Students studying linear algebra, mathematicians interested in dynamical systems, and educators teaching equilibrium concepts in mathematics.

cris623
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Homework Statement



Find the equilibrium state of the dynamical system

x1(t+1)=−05x1(t)−02x2(t)−1
x1(t+1)=26x1(t)+07x2(t)+1

the 1's and 2's after the x's are actually subscripts

I have no idea where to start with this. We did equilibrium systems in class but I've never seen the information represented this way and I have no idea where to start.
I'm more just looking for an explanation on how to read the equations.
Thanks in advance
 
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hi cris623! :smile:

(try using the X2 icon just above the Reply box :wink:)

hint: in equilibrium, x1(t+1) will be the same as x1(t), won't it? :wink:
 

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