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Next: 1.2.2 Qualitative analysis Up: 1.2 Two dimensional differential Previous: 1.2 Two dimensional differential

1.2.1 Examples

We looked at ``two toy neurons'' that are coupled together as an example:

$\displaystyle \left \{ \begin{array}{lc} \dot{v}_1 = -5v_1 + 17 \tan^{-1}(v1) -...
...  \dot{v}_2 = -v_2 + 4 \tan^{-1}(v1) -5 \tan^{-1}(v_2)  \end{array} \right.$    

We also looked at a pair of linear equations of the form:

$\displaystyle \left \{ \begin{array}{lc} \dot{v}_1(t) = a \cdot v_1(t) + b \cdo...
...  \dot{v}_2(t) = c \cdot v_1(t) + d \cdot v_2(t) + I_2  \end{array} \right.$    

With and without external inputs $ I_1,I_2$. We then saw that the equilibrium points of the linear system above (without external inputs) has the same behavior as the equilibrium point of the same system with external inputs.

Eran Borenstein