A Symbolic Solution Approach for Chaotic Induced Problems

This work investigates dynamical chaos of systems resulting from bifurcation of non-linear system. Dynamical behaviours of some complex nonlinear systems are considered. The work explores chaotic situations exhibiting irregular random behaviors due to the system ergodic properties. Therefore, a symbolic solution approach has been suggested. This approach includes a feedback control mechanism, discretization of the nonlinear coupled equation and the transformation of the nonlinear system into a linear periodic system. The solution starts with normalizing the dynamical control system using state space variables of the system dynamics and then linearized. The resulting system is transformed into special polynomials. The principles and concepts of chaos theory are relayed in the work. The results showed that the linearized system is asymptotically stable. An illustration is provided.