Balanced loss-gain induced chaos in a periodic Toda lattice

Abstract

We consider equal-mass periodic Toda oscillators with balanced loss-gain for two and three particles. The two-particle system is integrable. The three-particle equal-mass periodic Toda lattice is considered in presence of balanced loss-gain and velocity mediated coupling. The system is Hamiltonian for specific values of the coupling constants. The generalized momentum is the second integral of motion and study of Poincaré section indicates its integrability in certain region of the parameter-space. The generic model admits both non-chaotic and chaotic solutions. The chaos in the system with vanishing velocity mediated coupling is solely induced due to the presence of balanced loss-gain, since undriven equal-mass Toda lattice is non-chaotic. The chaotic behavior is studied in detail for the generic system.