We revisit the laser model with cavity loss modulation, from which evidence of chaos and generalized multistability was discovered in 1982 [1]. Multistability refers to the coexistence of two or more attractors in nonlinear dynamical systems. Despite its relative simplicity, the adopted model shows us how the multistability depends on the dissipation of the system. The model is then tested under the action of a secondary sinusoidal perturbation, which can remove bistability when a suitable relative phase is chosen [2]. Such a control strategy is universally known as “phase control” and it was first implemented in the same physical system but at different resonance frequencies [3].
The potential of this control technique has been validated on other paradigmatic chaotic systems such as the Duffing oscillator. In this particular case, it has been verified that the control is more sensitive when applied to the cubic term of the nonlinearity [4].
We recently demonstrated that phase control, which is classified as a nonfeedback method, can be converted to a closed loop control (feedback method) when a suitable adaptive filter is used on the chaotic signal to be processed [5].

References

[1] F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser,” Phys. Rev. Lett. 49(17), 1217–1220 (1982).
[2] R. Meucci, J.M. Ginoux, M. Mehrabbeik, S. Jafari, and J. C.Sprott” Generalized multistability and its control in a laser”: Chaos 32, 083111 (2022); doi: 10.1063/5.0093727.
[3] Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, “Experimental control of chaos by means of weak parametric perturbations,” Phys. Rev. E 49(4), R2528–R2531 (1994).
[4] R. Meucci, S. Euzzor, E. Pugliese, S. Zambrano, M. R. Gallas, and J. A. C. Gallas, “Optimal phase-control strategy for damped-driven Duffing oscillators,” Phys. Rev. Lett. 116(4), 044101 (2016).
[5] R. Meucci, S. Euzzor, M.Ciofini, A.Lapucci, and S. Zambrano” Demonstrating Filtered Feedback Control Near a Boundary Crisis” IEEE Trans. on Circuits and Systems¬ -I: 68(7), 3023 (2021).

Riccardo Meucci received the doctor degree in Physics in 1982 and the specialization degree in Optics (PhD), both from University of Florence, Italy. From 1984 to 1987, he was research fellow at the Istituto di Cibernetica of the National Research Council (CNR) of Italy. Since 1987, he joined with the National Institute of Optics, Firenze, Italy, where he holds the position of Research Director. He is also contract professor of physical optics and mathematical methods for optics at University of Firenze. Riccardo Meucci is associate editor for the International Journal of Bifurcation and Chaos (IJBC) from 1 January 2018.
His research interests include nonlinear dynamics, chaos, control of chaos, synchronization and infrared digital holography.
He is IEEE Senior Member since 17 November 2018.