Initial value problem small nonlinearity systems

A. The Initial Value Problem for a System with a Small Nonlinearity... 

Many coupled time dependent differential equations exhibit types of solutions known as chaotie behavior . In principle, the solution of an initial value differential equation problem is eompletely determined by the differential equation and the set of initial eonditions. However, for some types of coupled nonlinear differential equations an extremely small change in the initial conditions produces a very distinguishably different time behavior. Such systems are said to exhibit chaotic behavior. One sueh system of equations is the Lorentz equations defined by ... 

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