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Renormalization group based implicit function approach to connecting orbits
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DOI：10.1016/j.cnsns.2025.109548.png)
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Abstract
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• A novel implicit function approach based on the renormalization group (RG) method is employed to approximate the connecting orbits of a series of dynamical systems. And the coefficients in the relation function satisfy a set of linear equations. • If a system possesses unknown parameters, they can be determined by an error function, the minimization of which gives the required parameters values. • To the best of the authors’ knowledge, there is scarce work on obtaining exact solutions for dynamical systems using the RG method. In our manuscript, we successfully express the exact connecting orbits of a three-dimensional dynamical system with a RG based implicit function.
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