The Sprott jerk equations are examples of autonomous third-order ordinary differential equations in a single dependent variable,
with simple nonlinearities that can produce chaos. Primes
denote derivatives with respect to time 
. The third time derivative 
is the jerk.
Two quadratic examples and a cubic example are
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(1)
|
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(2)
|
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(3)
|
In the first equation, 
and 
give the translation 
of the example 
in Sprott (2000). The third equation
appears there with the coefficient 0.7.
For the second equation, setting 
and 
gives the equivalent first-order system
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(4)
|
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(5)
|
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(6)
|
Its vector field has constant divergence 
, so the flow contracts phase space volume for 
. Near 
, Sprott (1997) found a
strange attractor numerically and estimated
its largest Lyapunov characteristic
exponent as about 0.055.
