Abstract
This paper proposes the computation of homoclinic points using the particle swarm optimization (PSO) in 2-dimensional discrete dynamical systems. Homoclinic points are a qualitative indicator for the system analysis because their existence guarantees the occurrence of chaos. However, it has been hard to explore the exact homoclinic points because the conventional computation methods need too much precise initial values and so complicated derivatives on the points. In contrast, the PSO requires neither complicated derivatives nor exact initial values. Our method computes the homoclinic points by combining two PSOs without setting the exact initial values. We also conduct a numerical experiment with Hénon map and confirm the validity of the algorithm.
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