This paper focuses on the dynamic behavior of a magnetorheological fluid undergoing an unsteady oscillatory shear under the presence of an applied magnetic field. The problem is studied from a nonlinear mechanical system perspective using tools such as: analysis in the phase space, frequency response and neural networks for parameters identification. For this purpose several numerical simulations are performed to compute the motion of N magnetic rigid spheres suspendend in a Newtonian carrier liquid. The particles are neutrally buoyant and interact both hydrodynamically and magnetically throughout the process of dynamic simulation. We apply an external magnetic field together with an oscillatory shear. These two deterministic mechanisms compete with each other to align the particles in a preferential direction. The nonlinearities are introduced into the system due to particle-particle interaction. The intensity of the non-deterministic mechanisms is regulated by two physical parameters that appear in the present formulation. The numerical simulations are based on a sophisticated technique of Ewald sums that compute convergent hydrodynamic and magnetic interactions. A numerical research code developed by the authors is used for this purpose. The code is both accurate and computationally efficient. The present work intends to show that several tools, otherwise thought to be mostly applied to the dynamics of nonlinear systems, can be used to explore the physical behavior of wet suspensions in fluid mechanics. Moreover several details of the micromechanics of these complex materials are captured and physically interpreted through the use of the proposed tools. (C) 2016 Elsevier B.V. All rights reserved.