Time-dependent saddle-node bifurcation: Breaking time and the point of no return in a non-autonomous model of critical transitions.

[1]  Stanca M. Ciupe,et al.  Mathematical biology , 2021, Encyclopedia of Evolutionary Psychological Science.

[2]  J. Sieber,et al.  Early-warning indicators for rate-induced tipping. , 2015, Chaos.

[3]  Lei Dai,et al.  Relation between stability and resilience determines the performance of early warning signals under different environmental drivers , 2015, Proceedings of the National Academy of Sciences.

[4]  Sebastian Wieczorek,et al.  Parameter shifts for nonautonomous systems in low dimension: bifurcation- and rate-induced tipping , 2015, 1506.07734.

[5]  Rachel Kuske,et al.  Tipping Points Near a Delayed Saddle Node Bifurcation with Periodic Forcing , 2014, SIAM J. Appl. Dyn. Syst..

[6]  É. Plagányi,et al.  Ecosystem modelling provides clues to understanding ecological tipping points , 2014 .

[7]  Peter A. Jones At the tipping point for epigenetic therapies in cancer. , 2014, The Journal of clinical investigation.

[8]  Hong Qian,et al.  Stochastic phenotype transition of a single cell in an intermediate region of gene state switching. , 2013, Physical review letters.

[9]  Y. Tu,et al.  A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales , 2013, 1310.5585.

[10]  Ping Ao,et al.  A Theory of Mesoscopic Phenomena: Time Scales, Emergent Unpredictability, Symmetry Breaking and Dynamics Across Different Levels , 2013 .

[11]  Felix X.-F. Ye,et al.  Evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model. , 2013, Theoretical population biology.

[12]  William A Catterall,et al.  The Hodgkin-Huxley Heritage: From Channels to Circuits , 2012, The Journal of Neuroscience.

[13]  José A. Langa,et al.  Attractors for infinite-dimensional non-autonomous dynamical systems , 2012 .

[14]  Sui Huang,et al.  Tumor progression: chance and necessity in Darwinian and Lamarckian somatic (mutationless) evolution. , 2012, Progress in biophysics and molecular biology.

[15]  Lei Dai,et al.  Generic Indicators for Loss of Resilience Before a Tipping Point Leading to Population Collapse , 2012, Science.

[16]  Andressa Ardiani,et al.  The tipping point for combination therapy: cancer vaccines with radiation, chemotherapy, or targeted small molecule inhibitors. , 2012, Seminars in oncology.

[17]  H. Qian Cooperativity in cellular biochemical processes: noise-enhanced sensitivity, fluctuating enzyme, bistability with nonlinear feedback, and other mechanisms for sigmoidal responses. , 2012, Annual review of biophysics.

[18]  Kazuyuki Aihara,et al.  Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers , 2012, Scientific Reports.

[19]  Peter E. Kloeden,et al.  Nonautonomous Dynamical Systems , 2011 .

[20]  Sui Huang,et al.  Systems biology of stem cells: three useful perspectives to help overcome the paradigm of linear pathways , 2011, Philosophical Transactions of the Royal Society B: Biological Sciences.

[21]  Peter Cox,et al.  Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[22]  C. Kuehn A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics , 2011, 1101.2899.

[23]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[24]  C. Kuehn Scaling of saddle-node bifurcations: degeneracies and rapid quantitative changes , 2008, 0807.1546.

[25]  M. Kot Elements of Mathematical Ecology: Contents , 2001 .

[26]  H. Qian From discrete protein kinetics to continuous Brownian dynamics: A new perspective , 2001, Protein science : a publication of the Protein Society.

[27]  Grégoire Nicolis,et al.  Introduction to Nonlinear Science: References , 1995 .

[28]  Roy,et al.  Scaling laws for dynamical hysteresis in a multidimensional laser system. , 1995, Physical review letters.

[29]  S. Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[30]  F. Capra,et al.  The Turning Point: Science, Society and the Rising Culture , 1982 .

[31]  Richard Haberman,et al.  Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation Problems , 1979 .

[32]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[33]  Max J. Suarez,et al.  Simple albedo feedback models of the icecaps , 1974 .

[34]  Thomas C. Schelling,et al.  Dynamic models of segregation , 1971 .

[35]  Xiaoying Han,et al.  Applied Nonautonomous and Random Dynamical Systems , 2016 .

[36]  Peter E. Kloeden,et al.  Nonautonomous Dynamical Systems in the Life Sciences , 2013 .

[37]  F. Verhulst Differential Equations and Dynamical Systems , 2012 .

[38]  Ka Kit Tung,et al.  Topics in mathematical modeling , 2007 .

[39]  J. A. Kuznecov Elements of applied bifurcation theory , 1998 .

[40]  Thomas Erneux,et al.  Jump transition due to a time‐dependent bifurcation parameter: An experimental, numerical, and analytical study of the bistable iodate–arsenous acid reaction , 1991 .

[41]  Klaus Fraedrich,et al.  Catastrophes and resilience of a zero‐dimensional climate system with ice‐albedo and greenhouse feedback , 1979 .