The diffusion-driven instability and complexity for a single-handed discrete Fisher equation
暂无分享,去创建一个
[1] Yilun Shang. Global stability of disease-free equilibria in a two-group SI model with feedback control , 2015 .
[2] A. Kicheva,et al. Developmental Pattern Formation in Phases. , 2015, Trends in cell biology.
[3] Guang Zhang,et al. Turing instability and wave patterns for a symmetric discrete competitive Lotka-Volterra system , 2011 .
[4] K. Krischer,et al. Turing-Type Patterns on Electrode Surfaces , 2001, Science.
[5] Hamid Sabourian,et al. Bounded memory Folk Theorem , 2011, J. Econ. Theory.
[6] Anton Sergeev,et al. Diverse set of Turing nanopatterns coat corneae across insect lineages , 2015, Proceedings of the National Academy of Sciences.
[7] M. Cross,et al. Pattern formation outside of equilibrium , 1993 .
[8] S. Petrovskii,et al. Pattern formation in a space- and time-discrete predator–prey system with a strong Allee effect , 2012, Theoretical Ecology.
[9] Lingchong You,et al. Programmable assembly of pressure sensors using pattern-forming bacteria , 2017, Nature Biotechnology.
[10] H. I. Freedman. Deterministic mathematical models in population ecology , 1982 .
[11] Huayong Zhang,et al. Bifurcation, chaos and pattern formation in a space- and time-discrete predator-prey system , 2016 .
[12] Jean-Michel Grandmont. Nonlinear difference equations, bifurcations and chaos: An introduction , 2008 .
[13] Zhen Jin,et al. Pattern transitions in spatial epidemics: Mechanisms and emergent properties , 2016, Physics of Life Reviews.
[14] Yilun Shang. DISCRETE-TIME EPIDEMIC DYNAMICS WITH AWARENESS IN RANDOM NETWORKS , 2013 .
[15] Michael Heymann,et al. Testing Turing’s theory of morphogenesis in chemical cells , 2014, Proceedings of the National Academy of Sciences.
[16] Zhe Tan,et al. Polyamide membranes with nanoscale Turing structures for water purification , 2018, Science.
[17] S. Fortunato,et al. Statistical physics of social dynamics , 2007, 0710.3256.
[18] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.
[19] Yunjiang Rao,et al. Gate-tunable frequency combs in graphene–nitride microresonators , 2018, Nature.
[20] Gui‐Quan Sun,et al. Pattern dynamics in a Gierer–Meinhardt model with a saturating term , 2017 .
[21] Lu Zhang,et al. Turing instability for a two-dimensional Logistic coupled map lattice , 2010 .
[22] J. E. Pearson. Complex Patterns in a Simple System , 1993, Science.
[23] Pingzhou Liu,et al. A discrete model of competition , 1999 .
[24] Robert I. McKay,et al. Spatio-temporal dynamics and quantification of daisyworld in two-dimensional coupled map lattices , 2012 .
[25] H. Meinhardt,et al. A theory of biological pattern formation , 1972, Kybernetik.
[26] Xiaojie Hou,et al. Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system , 2019, Chaos, Solitons & Fractals.
[27] A. Hudspeth,et al. Reaction–diffusion model of hair-bundle morphogenesis , 2014, Proceedings of the National Academy of Sciences.
[28] A. Turing. The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.
[29] S. Petrovskii,et al. Spatiotemporal complexity of biological invasion in a space- and time-discrete predator–prey system with the strong Allee effect , 2012 .
[30] Wen-Chyuan Yueh. EIGENVALUES OF SEVERAL TRIDIAGONAL MATRICES , 2005 .
[31] J. Dunkel,et al. Curvature-induced symmetry breaking determines elastic surface patterns. , 2015, Nature materials.
[32] Yilun Shang,et al. Modeling epidemic spread with awareness and heterogeneous transmission rates in networks , 2013, Journal of biological physics.
[33] Ilan Koren,et al. A Satellite-Based Lagrangian View on Phytoplankton Dynamics. , 2018, Annual review of marine science.
[34] Guang Zhang,et al. Dependence of Initial Value on Pattern Formation for a Logistic Coupled Map Lattice , 2016, PloS one.
[35] Andrea R Tao,et al. Spontaneous formation of nanoparticle stripe patterns through dewetting , 2005, Nature materials.
[36] Khellil Sefiane,et al. Mechanisms of pattern formation from dried sessile drops. , 2018, Advances in colloid and interface science.
[37] Robert M. May,et al. Simple mathematical models with very complicated dynamics , 1976, Nature.
[38] F. Tito Arecchi,et al. PATTERN FORMATION AND COMPETITION IN NONLINEAR OPTICS , 1999 .
[39] Andrea J. Liu,et al. Spotted vesicles, striped micelles, and responsive Janus assemblies induced by ligand binding , 2009, Nature materials.
[40] Huayong Zhang,et al. Spatiotemporal complexity of a discrete space-time predator−prey system with self- and cross-diffusion , 2017 .
[41] L. Chi,et al. Advanced colloidal lithography: From patterning to applications , 2018, Nano Today.
[42] E. Vanden-Eijnden,et al. Emulsion patterns in the wake of a liquid–liquid phase separation front , 2018, Proceedings of the National Academy of Sciences.
[43] Y. Kuznetsov. Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.
[44] Vincent Noireaux,et al. Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells , 2017, Proceedings of the National Academy of Sciences.
[45] Guang Zhang,et al. Spiral patterns near Turing instability in a discrete reaction diffusion system , 2013 .
[46] Q Ouyang,et al. Pattern Formation by Interacting Chemical Fronts , 1993, Science.