We propose a dynamical model using traveling wave transformations from a three-component magnetized collisionless homogeneous plasma consisting of hot protons, hot heavier ions (He++), and kappa distributed electrons. The dynamical properties of the both perturbed and unperturbed dynamical systems are presented for both the slow and fast electrostatic structures. The external perturbation is a source of weak chaos, which can be quantified by the lyapunov exponents. It is also interesting to investigate how the fractal dimension changes with the initial conditions, whereas the parameters are fixed to some physical values. The results presented in the proposed study are relevant to the dynamical properties and fractal patterns of coherent electrostatic structures observed in the solar wind at 1 AU. © 2020 IOP Publishing Ltd.