Abstract
Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The probability characteristic of hyper-chaotic sequences produced by two dimensional hyper-chaotic discrete systems was analyzed. For the first time, a new method to find all solutions based on utilizing two dimensional probability hyper-chaotic discrete mapping to obtain initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.
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