Complexified Dynamical Systems

Understand

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric.

• The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions.
• This paper examines a subset of the complex solutions that contains the real solutions, namely, those having PT symmetry.
• The condition of PT symmetry selects out complex solutions that are periodic.