Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond

Landscape and flux theory of non-equilibrium dynamical systems with application to biology

(2015) Jin Wang   ADVANCES IN PHYSICS

Distinguishing the rates of gene activation from phenotypic variations

(2015) Ye Chen et al.   BMC Systems Biology

Stochastic Phenotype Transition of a Single Cell in an Intermediate Region of Gene State Switching

(2015) Hao Ge et al.   PHYSICAL REVIEW LETTERS

Energy Landscape Reveals That the Budding Yeast Cell Cycle Is a Robust and Adaptive Multi-stage Process

(2015) Cheng Lv et al.   PLoS Computational Biology

Summing over trajectories of stochastic dynamics with multiplicative noise

(2014) Ying Tang et al.   JOURNAL OF CHEMICAL PHYSICS

Construction of an Effective Landscape for Multistate Genetic Switches

(2014) Mingyang Lu et al.   PHYSICAL REVIEW LETTERS

Constructing the Energy Landscape for Genetic Switching System Driven by Intrinsic Noise

(2014) Cheng Lv et al.   PLoS One

Non-equilibrium transition state rate theory

(2014) Haidong Feng et al.   Chemical Science

Landscapes of non-gradient dynamics without detailed balance: Stable limit cycles and multiple attractors

(2012) Hao Ge et al.   CHAOS

Bistability, Bifurcations, and Waddington's Epigenetic Landscape

(2012) James E. Ferrell   CURRENT BIOLOGY

Beyond Itô versus Stratonovich

(2012) Ruoshi Yuan et al.   JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Quasi-potential landscape in complex multi-stable systems

(2012) J. X. Zhou et al.   Journal of the Royal Society Interface

The potential and flux landscape, Lyapunov function and non-equilibrium thermodynamics for dynamic systems and networks with an application to signal-induced Ca2+oscillation

(2012) Li Xu et al.   NONLINEARITY

The molecular and mathematical basis of Waddington's epigenetic landscape: A framework for post-Darwinian biology?

(2011) Sui Huang   BIOESSAYS

Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: Curvature, gauge field, and generalized fluctuation-dissipation theorem

(2011) Haidong Feng et al.   JOURNAL OF CHEMICAL PHYSICS

Stochastic theory of nonequilibrium steady states and its applications. Part I

(2011) Xue-Juan Zhang et al.   PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS

Quantifying the Waddington landscape and biological paths for development and differentiation

(2011) J. Wang et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Rediscovering Waddington in the post-genomic age

(2010) Heather A. Jamniczky et al.   BIOESSAYS

Kinetic paths, time scale, and underlying landscapes: A path integral framework to study global natures of nonequilibrium systems and networks

(2010) Jin Wang et al.   JOURNAL OF CHEMICAL PHYSICS

Transition times in the low-noise limit of stochastic dynamics

(2010) Sergey V. Malinin et al.   JOURNAL OF CHEMICAL PHYSICS

Mapping between dissipative and Hamiltonian systems

(2010) Jianhua Xing   Journal of Physics A-Mathematical and Theoretical

Potential and flux landscapes quantify the stability and robustness of budding yeast cell cycle network

(2010) J. Wang et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Thermodynamic Limit of a Nonequilibrium Steady State: Maxwell-Type Construction for a Bistable Biochemical System

(2009) Hao Ge et al.   PHYSICAL REVIEW LETTERS

The geometric minimum action method for computing minimum energy paths

(2008) Eric Vanden-Eijnden et al.   JOURNAL OF CHEMICAL PHYSICS

Potential landscape and flux framework of nonequilibrium networks: Robustness, dissipation, and coherence of biochemical oscillations

(2008) J. Wang et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA