Nonlinear and Non-local Models in Social and Ecological Systems

社会和生态系统中的非线性和非局部模型

• 批准号: 1909638
• 负责人: Nancy Rodriguez
• 金额: $ 30.18万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-06-15 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1909638&HistoricalAwards=false
• 关键词: Nonlinear; Non; local; Models; Social

The goal of this project is the introduction of a theoretical framework to understand and predict macroscopic patterns that are formed in many complex social and ecological systems. This research is motivated primarily be the two phenomena: the social and environmental interactions in social animals that lead to development of territorial patterns; development of urban gentrification patterns. Although conceptually different, these phenomena will be modeled by very similar mathematical models that fit into the framework of reaction-advection-diffusion (RAD) systems. RAD systems are the focus of this research; their use will help to gain insight into complex social and ecological systems where there is a need to understand macroscopic patterns. In this framework the PI will work on incorporating real-world data to extract objective information that will help shed light into what are the most influential factors leading to the complex patterns which are observed in ecology and sociology. Associated to this research project is a mentoring plan focused on advising underrepresented minority students at University of Colorado Boulder majoring in a STEM field. This will mainly be done through the initiation of a Society of Chicanos and Native Americans in the Science chapter. The aim is to provide these students with a network that can help them succeed in STEM. The overarching objective of this research is to develop, analyze, and simulate reaction-advection-diffusion (RAD) systems based on real-life observations and data. For example, RAD systems that are data-driven must include heterogeneities (spatial and temporal) as well as nonlocal operators, posing significant mathematical and computational challenges. RAD systems also provide a perfect framework to test hypothesis postulated by researchers in other fields, since their solutions can serve as a probability density function for the use of various methodologies, such as maximum likelihood estimation, to fit parameters to data. The PI will take advantage of this framework to develop an infrastructure (theory, algorithms, and software) targeted toward ecologists and social scientists that will validate RAD-type models by fitting them to data using appropriate statistical techniques. This research will contain three interrelated projects: the first one will be centered around the modeling of social and environmental interactions in social animals in order to understand territorial patterns through the use of non-local and heterogeneous RAD systems; the focal point of the second project will be on the development of a methodology and numerical framework to incorporate (social) data in order to test hypothesis developed by sociologists, with gentrification as a first case study; the final project will focus on developing the theory for non-local reaction-diffusion equations that arise from birth-jump processes, which are very suitable models for processes for which birth and dispersal cannot be separated.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的目的是引入一个理论框架，以理解和预测许多复杂的社会和生态系统中形成的宏观模式。这项研究主要是两种现象：社会动物的社会和环境互动导致领土模式的发展；城市高档化模式的发展。尽管在概念上有所不同，但这些现象将通过非常相似的数学模型来建模，这些模型适合反应 - 接地扩散（RAD）系统的框架。 RAD系统是这项研究的重点。它们的使用将有助于深入了解需要了解宏观模式的复杂社会和生态系统。在此框架中，PI将致力于合并现实世界数据以提取客观信息，以帮助阐明哪些最有影响力的因素导致生态学和社会学中观察到的复杂模式。 与该研究项目相关的是一项指导计划，重点是为科罗拉多大学博尔德大学专业的STEM领域专业的代表性不足的少数民族学生提供建议。 这将主要是通过科学章节中的奇卡诺斯和美洲原住民社会的启动来完成。 目的是为这些学生提供一个可以帮助他们在STEM中取得成功的网络。 这项研究的总体目的是基于现实观察和数据开发，分析和模拟反应 - 接地扩散（RAD）系统。 例如，数据驱动的RAD系统必须包括异质性（空间和时间）以及非本地运算符，带来重大的数学和计算挑战。 RAD系统还提供了一个完美的框架来检验其他领域研究人员假设的假设，因为它们的解决方案可以作为使用各种方法的概率密度函数，例如最大似然估计，以适合数据参数。 PI将利用该框架来开发针对生态学家和社会科学家的基础架构（理论，算法和软件），这些基础架构将通过使用适当的统计技术将其拟合到数据中来验证RAD型模型。 这项研究将包含三个相互关联的项目：第一个项目将集中在社会动物中社会和环境相互作用的建模围绕，以通过使用非本地和异构RAD系统来理解领土模式； 第二个项目的焦点将是开发方法和数值框架，以纳入（社会）数据，以测试社会学家开发的假设，而高档化为第一个案例研究；最终项目将着重于开发由出生跳跃过程引起的非本地反应扩散方程的理论，这些方程是针对无法分离出出生和分散的过程的非常合适的模型。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力和更广泛影响的评估来评估的支持，并被视为值得获得的支持。

项目成果

ON EQUILIBRIUM SOLUTIONS TO NONLOCAL MECHANISTIC MODELS IN ECOLOGY

• DOI: 10.11948/20200269
• 发表时间: 2021-12-01
• 期刊: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
• 影响因子: 1.1
• 作者: Ellefsen, Erin;Rodriguez, Nancy
• 通讯作者: Rodriguez, Nancy

Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation

• DOI: 10.1142/s0218202520500396
• 发表时间: 2020-05
• 期刊: Mathematical Models and Methods in Applied Sciences
• 影响因子: 3.5
• 作者: N. Rodríguez;M. Winkler

Understanding the Effects of On- and Off-Hotspot Policing: Evidence of Hotspot, Oscillating, and Chaotic Activities

• DOI: 10.1137/20m1359572
• 发表时间: 2021-01
• 期刊: SIAM J. Appl. Dyn. Syst.
• 作者: N. Rodríguez;Qi Wang;Lulu Zhang

Traveling wave solutions in a model for social outbursts in a tension‐inhibitive regime

紧张抑制政权中社会爆发模型中的行波解决方案

• DOI: 10.1111/sapm.12394
• 发表时间: 2021
• 期刊: Studies in Applied Mathematics
• 影响因子: 2.7
• 作者: Bakhshi, Marzieh;Ghazaryan, Anna;Manukian, Vahagn;Rodriguez, Nancy
• 通讯作者: Rodriguez, Nancy

THE EFFECT OF DIRECTED MOVEMENT ON THE STRONG ALLEE EFFECT

• DOI: 10.1137/20m1330178
• 发表时间: 2021-01-01
• 期刊: SIAM JOURNAL ON APPLIED MATHEMATICS
• 影响因子: 1.9
• 作者: Cosner, Chris;Rodriguez, Nancy
• 通讯作者: Rodriguez, Nancy