Search

In many asymptotically stable fluid systems, arbitrarily small fluctuations can grow by orders of magnitude before eventually decaying, dramatically enhancing the fluctuation variance beyond the minimum predicted by linear stability theory. Here using influential quantitative models drawn from the mathematical biology literature, we establish that dramatic amplification of arbitrarily small fluctuations is found in excitable cell signaling systems as well. Our analysis highlights how positive and negative feedback, proximity to bifurcations, and strong separation of timescales can generate nontrivial fluctuations without nudging these systems across their excitation thresholds. These insights, in turn, are relevant for a broader range of related oscillatory, bistable, and pattern-forming systems that share these features. The common thread connecting all of these systems with fluid dynamical examples of noise amplification is non-normality.

Cell physiology is orchestrated, on a molecular level, through complex networks of biochemical reactions. The propagation of random fluctuations through these networks can significantly impact cell behavior, raising challenging questions about how network design shapes the cell's ability to suppress or exploit these fluctuations. Here, drawing on insights from statistical physics, fluid dynamics, and systems biology, we explore how transient amplification phenomena arising from network connectivity naturally limit a biochemical system's ability to suppress small fluctuations around steady-state behaviors. We find that even a simple system consisting of two variables linked by a single interaction is capable of amplifying small fluctuations orders of magnitude beyond the levels predicted by linear stability theory. We also find that adding additional interactions can promote further amplification, even when these interactions implement classic design strategies known to suppress fluctuations. These results establish that transient amplification is an essential factor determining baseline noise levels in stable intracellular networks. Significantly, our analysis is not bound to specific systems or interaction mechanisms: we find that noise amplification is an emergent phenomenon found near steady states in any network containing sufficiently strong interactions, regardless of its form or function.

While topological defects are essential to our understanding of self-organizing periodic systems, little is known about how these systems respond when their defects are subjected to geometrical constraints. In an experiment on spatially modulated thermal convection patterns, we observe that applied geometrical constraints bind topological defects into robust self-localized structures that evolve through aggregation, annihilation, and self-replication. We demonstrate that this unexpected cooperative response to the modulation is a natural consequence of three generic elements: phase locking, symmetry breaking, and spatial resonance. Our work provides new insights into the interplay between order, chaos, and control in self-organizing systems.

We report experiments on spatially forced inclined layer convection, where the combined effect of the intrinsic symmetry breaking due to a gravity-induced shear flow and spatially periodic 1D forcing is studied. We observed pattern selection processes resulting in stabilization of spatiotemporal chaos and the emergence of novel two-dimensional states. Phase diagrams depicting the different observed states for typical forcing scenarios are presented. Convection in the weakly nonlinear regime is compared with theory, and a good agreement is found.

The identification of general principles relating structure to dynamics has been a major goal in the study of complex networks. We propose that the special case of linear network dynamics provides a natural framework within which a number of interesting yet tractable problems can be defined. We report the emergence of modularity and hierarchical organization in evolved networks supporting asymptotically stable linear dynamics. Numerical experiments demonstrate that linear stability benefits from the presence of a hierarchy of modules and that this architecture improves the robustness of network stability to random perturbations in network structure. This work illustrates an approach to network science which is simultaneously structural and dynamical in nature.