Synchronized movement of (both unicellular and multicellular) systems can be observed almost everywhere. Understanding of how organisms are regulated to synchronized behavior is one of the challenging issues in the field of collective motion. It is hypothesized that one or a few agents in a group regulate(s) the dynamics of the whole collective, known as leader(s). The identification of the leader (influential) agent(s) is very crucial. This article reviews different mathematical models that represent different types of leadership. We focus on the improvement of the leader-follower classification problem. It was found using a simulation model that the use of interaction domain information significantly improves the leader-follower classification ability using both linear schemes and information-theoretic schemes for quantifying influence. This article also reviews different schemes that can be used to identify the interaction domain using the motion data of agents.
Collective migration of cells is a fundamental behavior in biology. For the quantitative understanding of collective cell migration, live-cell imaging techniques have been used using e.g., phase contrast or fluorescence images. Particle tracking velocimetry (PTV) is a common recipe to quantify cell motility with those image data. However, the precise tracking of cells is not always feasible. Particle image velocimetry (PIV) is an alternative to PTV, corresponding to Eulerian picture of fluid dynamics, which derives the average velocity vector of an aggregate of cells. However, the accuracy of PIV in capturing the underlying cell motility and what values of the parameters should be chosen is not necessarily well characterized, especially for cells that do not adhere to a viscous flow. Here, we investigate the accuracy of PIV by generating images of simulated cells by the Vicsek model using trajectory data of agents at different noise levels. It was found, using an alignment score, that the direction of the PIV vectors coincides with the direction of nearby agents with appropriate choices of PIV parameters. PIV is found to accurately measure the underlying motion of individual agents for a wide range of noise level, and its condition is addressed.
This study examines a discrete-time enzyme model with Caputo fractional order. We look into the existence and uniqueness of fixed points in the discrete dynamic model and discover parametric criteria for their local asymptotic stability. Additionally, it is demonstrated using bifurcation theory that the system experiences Period-Doubling and Neimark-Sacker bifurcation in a constrained area around the singular positive fixed point and that an invariant circle would result. It has been determined that the parameter values and the initial conditions have a significant impact on the dynamical behavior of the fractional order enzyme model. Additionally, with the use of Matlab tools, numerical analysis is offered to illustrate the theoretical debates. Therefore, numerical simulations are used to support the key theoretical findings.
In order to investigate sediment-loading processes in a catchment, the daily time series of river discharge and sediment load were applied to a semi-distributed model, the Soil and Water Assessment Tool (SWAT). The time series of discharge and sediment load were obtained by monitoring the river stage and water turbidity of the Oikamanai River, Hokkaido, Japan, in the rainfall season (April-November) of 2011-2014. The catchment is forested (ca 90% area) but underlain by the Neogene sedimentary rocks with currently active faults and forest soils with tephra layers, which tend to frequently produce slope failure such as landslide and bank collapse by rainfall or snowmelt. The water turbidity, T, in ppm was converted into suspended sediment concentration, SSC, in g/L by applying the linear relationship between T and SSC. The acquisition of the time series of discharge, Q (m 3 /s) and sediment load, L (=Q•SSC in g/s) of the river allowed us to distinguish the fluvial sediment transport, accompanied by slope failure in the upstream, from that under no slope failure. The SWAT was used to simulate soil erosion and identify the region prone to the soil erosion in the Oikamanai River basin. The model's results showed a satisfactory agreement between daily observed and simulated sediment load as indicated by the high Nash-Sutcliffe efficiency. This evidences that the upper mountainous region of the catchment provides a main sediment source, accompanied by slope failure.
In this paper, we extract some novel solitary wave solutions in terms of hyperbolic functions to the Jimbo-Miwa model. The sine-Gordon expansion method is used to investigate the proposed model. By using graphical analysis, we show the impact the solution’s which are very impactful to explain the nature of the solitary wave. We believe that the findings of the current work will be useful in the field of solitons and solitary waves.
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