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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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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Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics by Till D. Frank

“…In the present study, properties of mathematical models of bistable signaling pathways are examined from the perspective of synergetics, a theory of self-organization and pattern formation founded by Hermann Haken. At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. …”
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A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term by Shengmao Fu, Ji Liu

“…Our results provide a mathematical description for early pattern formation in the model.…”
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The impact of immune cell interactions on virus quasi-species formation by Ali Moussaoui, Vitaly Volpert

“…Numerical simulations were employed to elucidate the nonlinear dynamics and pattern formation inherent in the nonlocal model.…”
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Observation of Pattern Stabilization in a Driven Superfluid by Nikolas Liebster, Marius Sparn, Elinor Kath, Jelte Duchene, Keisuke Fujii, Sarah L. Görlitz, Tilman Enss, Helmut Strobel, Markus K. Oberthaler

“…While the early phase of pattern formation can be understood on the basis of linear stability analyses, the longtime dynamics can only be described by accounting for the interactions between the excitations generated by the drive. …”
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Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion by Caiyun Wang, Yongyong Pei, Yaqun Niu, Ruiqiang He

“…Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. …”
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Spatial Complexity of a Predator-Prey Model with Holling-Type Response by Lei Zhang, Zhibin Li

“…Based on the stability and bifurcation analysis, we obtain spiral pattern formation via numerical simulation. Additionally, we study the model with a color noise and external periodic forcing. …”
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