A hamiltonian path is a path walk P that can be a hamiltonian path or hamiltonian circuit. Determining whether such hamiltonian path exists in a given graph G = (V, E) is a NP-Complete problem. In this paper, a novel algorithm with chaotic behaviour for hamiltonian path problem is proposed. We show that our algorithm runs in $O(V^5(V + E))$ for hard sparse instances from FHCP challenge dataset.