We introduce a new three-dimensional autonomous system obtained by adding acubic damping term and a cross-coupling nonlinearity to the classical R¨ossler equations.The system is motivated by a simple physical model of a damped driven oscillator withnonlinear feedback. Through numerical integration we find a chaotic attractor forparameters a = 0.10, b = 0.2, c = 5.7, d = 0.20, e = 0.01. The largest Lyapunovexponent is λ1 ≈ 0.0159, confirming chaos, and the power spectrum is broadband.Equilibrium analysis reveals two saddle-focus fixed points. A bifurcation diagram asa function of d shows a period-doubling route to chaos, and a parameter-space heatmap in the (d, e) plane identifies the chaotic region. The full Lyapunov spectrum is(λ1, λ2, λ3) = (0.0159,−0.00957,−18.98), yielding a Kaplan–Yorke dimension DKY ≈2.0003. Searches in major databases yielded no identical system, indicating novelty.We propose to name this new chaotic attractor the Tatvamasi attractor.
Rishabh Mehta (2026) studied this question.