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Chaotic Behaviour In Three Dimensional Quadratic Systems., Fu Zhang

Student Work

This thesis presents a part of the proof of that there is no chaos in three dimensional autonomous quadratic systems of four terms with one nonlinear term and without constant terms. The first step of the proof is identifying equivalent systems from all possible systems by the 3rd order permutation group and as a result 138 inequivalent patterns are found(refer to appendix A). And then for the solvable systems we show how to solve them. Some of the nonsolvable systems turn out to be 2nd order autonomous systems and they are resolved by analyzing the monotonicity of the solutions and/or …