Related papers: Lag-Induced Critical Transitions to Extinction in …
We present a novel exactly solvable ordinary differential equation model for rate-induced tipping: a dynamic phenomenon of dynamical systems where a time-dependent parameter triggers the transition of stability of a system. Our model…
We consider measurement-induced phase transitions in monitored quantum circuits with a measurement rate that fluctuates in time, remaining spatially uniform at each time. The spatially correlated fluctuations in the measurement rate disrupt…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may…
We explore the critical behaviors in the dynamics of information transfer of a biologically-inspired system by an individual-based model. "Quorum response", a type of social interaction which has been recognized taxonomically in animal…
We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distributive lattice; the fitness landscape is a real-valued…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
Detection of critical slowing down (CSD) is the dominant avenue for anticipating critical transitions from noisy time-series data. Most commonly, changes in variance and lag-1 autocorrelation [AC(1)] are used as CSD indicators. However,…
We consider a null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree in the (sub)-diffusive regime and we prove that properly renormalized, the local time in a critical generation converges in law towards some function of…
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
On the basis of a lattice gas model and the convolution formula with cell construction scheme, we demonstrate that intermittency in the rapidity-space with respect to the scaled moments comes from a phase transition between ordered phase…
In fast growing bacteria, ribosomal RNA (rRNA) is required to be transcribed at very high rates to sustain the high cellular demand on ribosome synthesis. This results in dense traffic of RNA polymerases (RNAP). We developed a stochastic…
We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law,…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…
Experimental evidence of an absorbing phase transition, so far associated with spatio-temporal dynamics is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed opto-electronic feedback and…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…
Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and…