Abstract
Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.
Highlights
Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest
Our Faraday wave experiments explicitly show that the band gap opening that leads to the desirable stabilization of homogeneous states can be implemented with the introduction of appropriately designed system heterogeneity
These results show the existence of homogeneous states that persist in spite of heterogeneity but are promoted by it
Summary
Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. We show that for parametrically-driven systems in particular, the introduction of constrained but appropriately designed heterogeneity provides a general means to stabilize homogeneous states for a wide range of parameter values Because such homogeneous states emerge without the need for feedback control, HSHS can be exploited to design non-feedback control for complex systems, which has attracted interest in the past for the potential to suppress chaos[10]. Faraday wave experiments are usually performed using a flat substrate for the bottom of the container, which guarantees that the system is spatially homogeneous and has translational symmetry (up to boundary effects) This symmetry is spontaneously broken by the standing waves that are created by parametric resonance above the instability boundary. We show how heterogeneity from more general substrate geometries can impact the onset of Faraday wave instabilities, which allows us to experimentally demonstrate the existence of HSHS for both sinusoidal and random substrates with suitably large heterogeneity
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