The role of feedback in the formation of morphogen territories by David Iron, Adeela Syed, Heidi Theisen, Tamas Lukacsovich, Mehrangiz Naghibi, Lawrence J. Marsh, Frederic Y. M. Wan, Qing Nie

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An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems by Chichia Chiu, Jui-Ling Yu

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Spatially Distributed Morphogen Production and Morphogen Gradient Formation by Arthur D. Lander, Qing Nie, Frederic Y. M. Wan

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Spatiotemporal complexity in a predator--prey model with weak Allee effects by Yongli Cai, Malay Banerjee, Yun Kang, Weiming Wang

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Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells by Marcello Delitala, Tommaso Lorenzi

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Fingerprints of surface flows on solid substrates ablated by phase change: from laboratory experiments to planetary landscapes by Carpy, Sabrina, Berhanu, Michael, Chaigne, Martin, Courrech du Pont, Sylvain

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On a diffusive predator-prey model with nonlinear harvesting by Peng Feng

Subjects: “…pattern formation…”
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Prey-Taxis vs. An External Signal: Short-Wave Asymptotic and Stability Analysis by Andrey Morgulis, Karrar H. Malal

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Effects of initial vegetation heterogeneity on competition of submersed and floating macrophytes by Linhao Xu, Donald L. DeAngelis

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The resonance phenomenon in the reaction–diffusion systems by A. I. Lebanov, A. P. Chernyaev, T. K. Starozhilova

“…A new mechanism of pattern formation different from the Turing and oscillatory instabilities in the reaction–diffusion systems was found. …”
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Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion by Lei Zhang

“…Based on the bifurcation analysis (Hopf and Turing), we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point (u2*,v2*,w2*), and find that the model dynamics exhibits complex pattern replication. …”
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How the tulip breaking virus creates striped tulips by Aidan A. Wong, Gustavo Carrero, Thomas Hillen

“…A good understanding of the mechanism driving the striped pattern formation of broken tulips has been missing since the 17th century. …”
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Theoretical Study on Self-Organization of Vegetation Patterns Triggered by Water Resource in Deposited Sediment Layer by Tousheng Huang, Huayong Zhang, Zhao Liu, Ge Pan, Xiumin Zhang, Zichun Gao

“…With employment of the model, the conditions for pattern formation of the considered ecological system are determined via Turing instability analysis. …”
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Interactions with iridophores and the tissue environment required for patterning melanophores and xanthophores during zebrafish adult pigment stripe formation. by Larissa B Patterson, David M Parichy

“…Skin pigment patterns of vertebrates are a classic system for understanding fundamental mechanisms of morphogenesis, differentiation, and pattern formation, and recent studies of zebrafish have started to elucidate the cellular interactions and molecular mechanisms underlying these processes. …”
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Self-Organized Crystallization Patterns from Evaporating Droplets of Common Wheat Grain Leakages as a Potential Tool for Quality Analysis by Maria Olga Kokornaczyk, Giovanni Dinelli, Ilaria Marotti, Stefano Benedettelli, Daniele Nani, Lucietta Betti

“…We studied the evaporation-induced pattern formation in droplets of common wheat kernel leakages prepared out of ancient and modern wheat cultivars as a possible tool for wheat quality analysis. …”
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Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model by Zhenhua Bao, He Liu

“…By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These results suggest the existence of oscillatory patterns if the system parameters fall into certain parameter ranges. …”
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Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model by Xiaoqin Wang, Yongli Cai

“…We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. …”
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Traveling bands for the Keller-Segel model with population growth by Shangbing Ai, Zhian Wang

“…The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands.…”
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Group Classification of a Generalized Lane-Emden System by Ben Muatjetjeja, Chaudry Masood Khalique, Fazal Mahmood Mahomed

“…We perform the group classification of the generalized Lane-Emden system xu′′+nu′+xHv=0,  xv′′+nv′+xgu=0, which occurs in many applications of physical phenomena such as pattern formation, population evolution, and chemical reactions. …”
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Adaptive Optimal 𝑚-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems by Jui-Ling Yu

“…We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems. To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. …”
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