# Calculation of Lyapunov exponents for infinite systems of differential equations

Can you give an example of a function $\varphi$ and sequences $\{b_{i}\}$ and $\{a_{ij}\}$ for which one can calculate Lyapunov exponents of such the infinite system of differential equations and detect route to chaos in this dynamical system? $$\frac{du_{i}}{dt}=-b_{i}u_{i}+\varphi\Big(\sum_{j=1\atop j\neq i}^{\infty}a_{ij}u_{j}\Big),\quad i=1,2,\ldots$$ Here $b_{i}>0$ for all $i$.

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