Controlling hyperchaos in a multimode laser model

We show that it is possible to stabilize remnants of periodic orbits in a hyperchaotic system (with more than one positive Lyapunov exponent) using a single feedback parameter. Numerical simulations of a multimode laser with an intracavity frequency doubling crystal using occasional proportional feedback indicate that the controlled periodic orbits are locally unstable in only one coordinate, even though the system has three positive Lyapunov exponents in this parameter regime. This situation should be common in dynamical systems of the coupled oscillator type with many degrees of freedom.