Delay-induced multistability and offset boosting in the Tatvamasi chaotic attractor

The Tatvamasi attractor is a recently discovered three-dimensional chaotic flowbelonging to the R¨ossler family. In this work we uncover two fundamental propertiesof this system. First, adding a time-delayed feedback to the y equation induces robustmultistability: two distinct chaotic attractors coexist for the same parameters. Second,we show that the system possesses offset boosting – adding a constant k to the x variableshifts the attractor linearly without changing its dynamics. This property is provedanalytically and leads to extreme multistability: a continuous family of coexistingchaotic attractors parameterised by k. Numerical simulations confirm that the largestLyapunov exponent remains positive across a wide range of delays and offsets, and thatthe mean value of x shifts linearly with k. These results establish the Tatvamasi systemas a rich platform for studying delayed dynamics, multistability, and symmetry-likeinvariance.