Chaotic behavior of modified stretch-twist-fold (STF) flow with fractal property

In this paper, a modified stretch-twist-fold (STF) flow is introduced, which is based on STF flow that is associated with fluid particle motion that naturally arises in the dynamo theory. Dynamo theory intends a some typical procedure which follows the celestial bodies, such as earth, sun and other stars; due to this mechanism, they can maintain and amplify the magnetic field continuously. Chaoticity of modified STF attractor is discussed for different values of chaotic parameter. With the help of fractal process based on the modified STF flow, a multi-wing modified STF flow is obtained that gives a 2n-wing modified STF flow system. The Hamiltonian energy function of modified STF flow concludes that the energy is decreased as the number of multi-wing increases. Moreover, with the help of Melnikov technique and Hamiltonian energy function, existence of periodic solutions for modified STF flow is derived analytically.