Controlled destruction of chaos in the multistable regime

Drive-specific selection in multistable mechanical networks

Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.

Control of birhythmicity through conjugate self-feedback: Theory and experiment

Birhythmicity arises in several physical, biological, and chemical systems. Although many control schemes have been proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis, and experimental demonstrations, we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows a transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.

Control of stochastic multistable systems: experimental demonstration

Stochastic disturbances and spikes (sudden sharp fluctuations of any system parameter), commonly observed among natural and laboratory-scale systems, can perturb the multistable dynamics significantly and become a serious impediment when the device is designed for a certain dynamical behavior. We experimentally demonstrate that suitable periodic modulation of any system parameter may efficiently control such stochastic multistability related problems. The control mechanism is verified individually with two standard models (namely, an analog circuit of Lorenz equations and a cavity-loss modulated CO2 laser), against three externally introduced disturbing signals, (namely, white Gaussian noise, pink noise, and train of spikes). Indeed, with both the systems, it has been observed that the modulation is capable to significantly control untoward jumps to coexisting attractors that otherwise would have occurred due to either of the disturbances. These results establish the robustness and wide applicability of this control mechanism in resolving stochastic multistability related problems.

Control of multistate hopping intermittency

In multistable regimes, noise can create "multistate hopping intermittency," i.e., intermittent transitions among coexisting stable attractors. We demonstrate that a small periodic perturbation can significantly control such hopping intermittency. By "control" we imply a qualitative change in the probability distribution of occupation in the phase space around the stable attractors. In other words, if the uncontrolled system exhibits a preference to stay around a given attractor (say " A ") in comparison to another attractor (say " B "), the control perturbation creates a contrasting scenario so that attractor B is most frequently visited and consequently, the occupation probability becomes maximum around B instead of A . The control perturbation works in the following way: It destroys attractor A by boundary crisis while attractor B remains stable. As a result, even if the system is pushed by noise into the erstwhile basin of attractor A , the system does not remain there for long and therefore stays longer around attractor B . Significantly, such a change in the intermittent scenario can be obtained by a small-amplitude and slow-periodic perturbation. The control is theoretically demonstrated with two standard models, namely, Lorenz equations (for autonomous systems), and the periodically driven, damped Toda oscillator (for nonautonomous systems). Recent experiments with a cavity-loss modulated CO2 laser and an analog circuit of Lorenz equations have validated our theoretical demonstrations excellently.