The Tatvamasi attractor: a new chaotic attractor in a modified Rössler system with cubic dissipation

We introduce a new three-dimensional autonomous system obtained by adding a cubic 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 with nonlinear feedback. Through numerical integration we find a chaotic attractor for parameters a = 0.10, b = 0.2, c = 5.7, d = 0.20, e = 0.01. The largest Lyapunov exponent is λ1 ≈ 0.0148, confirming chaos, and the power spectrum is broadband. Equilibrium analysis reveals two saddle-focus fixed points. A bifurcation diagram as a function of d shows a period-doubling route to chaos, and a parameter-space heat map in the (d, e) plane identifies the chaotic region. The Kaplan–Yorke dimension is estimated as DKY ≈ 2.0006. Searches in major databases yielded no identical system, indicating novelty. We propose to name this new chaotic attractor the Tatvamasi attractor.