Phase diagram for a logistic system under bounded stochasticity
Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined effect of demographic and bounded environmental stochasticity. Three phases are identified: an inactive phase where the mean time to extinction $T$ increases logarithmically with the initial population size, an active phase where $T$ grows exponentially with the carrying capacity $N$, and temporal Griffiths phase, with power-law relationship between $T$ and $N$. The system supports an exponential phase only when the noise is bounded, in which case the continuum (diffusion) approximation breaks down within the Griffiths phase. This breakdown is associated with a crossover between qualitatively different survival statistics and decline modes. To study the power-law phase we present a new WKB scheme which is applicable both in the diffusive and in the non-diffusive regime.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A New Algorithmic Decision for Categorical Syllogisms via Caroll's Diagrams
In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categori…
Logical ReasoningvalidMatPhaseBench: A Semantics-Guided Benchmark for Materials Phase Diagrams Understanding
Materials phase diagrams are a core knowledge representation in materials science, encoding temperature,composition, phase stability, and phase transformation pathways, with their full understanding requiring thermodynam…
Do Diagrams Help Large Language Models Reason? Evidence from Syllogistic Reasoning
Diagrams are widely used to support logical reasoning, and prior studies suggest that representations such as Euler diagrams can improve human reasoning performance. Recent work has also explored their effects on large l…
Logical ReasoningOn Uniform Boundedness Properties of SGD and its Momentum Variants
A theoretical, and potentially also practical, problem with stochastic gradient descent is that trajectories may escape to infinity. In this note, we investigate uniform boundedness properties of iterates and function va…
regressionRetrievalaLLoyM: A large language model for alloy phase diagram prediction
Large Language Models (LLMs) are general-purpose tools with wide-ranging applications, including in materials science. In this work, we introduce aLLoyM, a fine-tuned LLM specifically trained on alloy compositions, tempe…