{"id":408,"date":"2023-04-19T09:18:22","date_gmt":"2023-04-19T13:18:22","guid":{"rendered":"https:\/\/systems.jhu.edu\/gonzalo\/?page_id=408"},"modified":"2024-03-26T19:34:01","modified_gmt":"2024-03-26T23:34:01","slug":"system-dynamics","status":"publish","type":"page","link":"https:\/\/systems.jhu.edu\/gonzalo\/system-dynamics\/","title":{"rendered":"System Dynamics"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">System Dynamics (SD) is an analysis paradigm for complex problem elicitation and policy design. Its modus operandi essentially consists of three phases: (1) a qualitative analysis of problems with a Systems Thinking framework to identify and map problem inputs, outputs, levels, interrelations, uncertainties, inconsistencies, etc. and (2) a quantitative phase in which qualitative maps are reduced to a set of mathematical entities (flows, levels, feedback loops, and delays) which end up in the assemblage of a system of coupled differential equations. Finally, (3) mathematical simulations are conducted on the model to study what changes in behavior are effectuated by changes in structure. SD is applied to attack problems exhibiting dynamical behavior in the engineering, social, management, economic, epidemiological, and physiological systems. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Syllabus (annually dynamic!)<\/h3>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"721\" src=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-6-1024x721.png\" alt=\"\" class=\"wp-image-448\" style=\"width:677px;height:476px\" srcset=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-6-1024x721.png 1024w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-6-300x211.png 300w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-6-768x541.png 768w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-6-1536x1081.png 1536w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-6.png 1838w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Case studies from class<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Below some images from the problems studied in class.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"582\" src=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/sd_model_shocks-1024x582.png\" alt=\"\" class=\"wp-image-675\" style=\"width:758px;height:auto\" srcset=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/sd_model_shocks-1024x582.png 1024w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/sd_model_shocks-300x171.png 300w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/sd_model_shocks-768x437.png 768w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/sd_model_shocks-1536x873.png 1536w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/sd_model_shocks-2048x1164.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A supply chain problem that exhibits the inventory behavior to external shocks.  <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1024\" src=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-1000x1024.png\" alt=\"\" class=\"wp-image-410\" style=\"aspect-ratio:0.9769820971867008;width:440px;height:auto\" srcset=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-1000x1024.png 1000w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-293x300.png 293w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-768x786.png 768w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-1500x1536.png 1500w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image.png 1506w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A classical ODE (predator\/prey) problem modeled using System Dynamic (above) and behavior of equation parameters (below).  <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"804\" src=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/image-3-1024x804.png\" alt=\"\" class=\"wp-image-667\" style=\"width:448px;height:auto\" srcset=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/image-3-1024x804.png 1024w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/image-3-300x236.png 300w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/image-3-768x603.png 768w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/image-3-1536x1206.png 1536w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2024\/03\/image-3.png 1898w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">An interesting staffing problem with several subtleties.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"953\" height=\"1024\" src=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-3-953x1024.png\" alt=\"\" class=\"wp-image-420\" style=\"width:396px;height:426px\" srcset=\"https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-3-953x1024.png 953w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-3-279x300.png 279w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-3-768x826.png 768w, https:\/\/systems.jhu.edu\/gonzalo\/wp-content\/uploads\/2023\/04\/image-3.png 1146w\" sizes=\"auto, (max-width: 953px) 100vw, 953px\" \/><figcaption class=\"wp-element-caption\">SD model to test effects of different policies on a firm hiring problem<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">More info<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Taught in the Spring Semester at Homewood Campus<\/li>\n\n\n\n<li>Prereqs: Calculus II, some Probability and Simulation courses <\/li>\n\n\n\n<li>Grade: (1) One Exam, (2) Homework Assignments, (3) Final project, (4) Participation in Class<\/li>\n\n\n\n<li>Textbook: Chapters and Papers assigned.<\/li>\n\n\n\n<li>Software: Vensim, Matlab, R<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>System Dynamics (SD) is an analysis paradigm for complex problem elicitation and policy design. Its modus operandi essentially consists of three phases: (1) a qualitative analysis of problems with a Systems Thinking framework to identify and map problem inputs, outputs, levels, interrelations, uncertainties, inconsistencies, etc. and (2) a quantitative phase in which qualitative maps are [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-408","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/pages\/408","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/comments?post=408"}],"version-history":[{"count":14,"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/pages\/408\/revisions"}],"predecessor-version":[{"id":679,"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/pages\/408\/revisions\/679"}],"wp:attachment":[{"href":"https:\/\/systems.jhu.edu\/gonzalo\/wp-json\/wp\/v2\/media?parent=408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}