Rössler

The Rössler attractor is a chaotic, three-dimensional continuous-time dynamical system named after Otto E. Rössler, who introduced it in 1976. It is widely studied as a canonical example of deterministic chaos and serves as a reference model in nonlinear dynamics.

It is defined by a set of ordinary differential equations: dx/dt = -y - z, dy/dt = x + a y, dz/dt = b + z(x - c), where a, b, c are real parameters. For common choices such as a = 0.2, b = 0.2, c = 5.7, the system exhibits chaotic behavior; varying the parameters can change the dynamics and the geometry of the attractor.

The Rössler attractor is characterized by a strange attractor with fractal geometry and sensitive dependence on initial conditions. It is often visualized as a rotating, ribbon-like structure around a central axis. Depending on parameter values, the attractor can have a single dominant lobe, and its shape may vary with changes in the parameters.

Applications of the Rössler system include studies of chaos theory, synchronization, and secure communications, as well as serving as a teaching example for numerical integration of nonlinear ordinary differential equations. It is commonly simulated with standard numerical methods such as Runge-Kutta, and its simple form makes it convenient for software demonstrations and visualization of chaotic dynamics.