# Digital Representation of a Nonlinear ODE with Small Differences in Initial Conditions

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The graphic on the left overlays the plots of the solutions of a nonlinear ODE with 50 slightly different initial conditions.

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Contributed by: Stella Chuyue Dong and Vitaliy Kaurov (December 2012)

Created at the 2011 NKS Summer School (*NKS|Online*)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Given a nonlinear ODE of the form , where , this Demonstration evolves the equation in time, assuming initial to be fixed.

With the advent of chaos (obtained by increasing the forcing parameter ), the digital representation loses its coherence, indicating a divergence between the solutions proportional to its Lyapunov measure.

## Permanent Citation