A hybrid chaos: a novel 3D strange attractor in a coupled Tinkerbell-Duffing-Jerk system with external forcing

The purpose of this study is to find hybrid nonlinear dynamical system, combining elements of systems such as Tinkerbell, Duffing, and Jerk, with the addition of periodic external excitation terms (cos(t), sin(t)). The system was analysed using chaos theory tools, such as: fixed points and stability analysis (Newton-Raphson method). phase space and a strange attractor were used to clarify the fractal structure. Correlation dimension (D) and Lyapunov indices were used to evaluate complexity and sensitivity to initial conditions. Nonlinear interactions such as( , , 2 ) were the main factor in shaping the dynamic distortions and complexity of the attractor. Periodic external excitations enhanced instability and increased the sensitivty of the system, contributing to a higher D .The system can be used to generate secure random keys and to model natural phenomena, such as fluctuations in environmental or financial systems.