1.0SOUL OF MATHEMATICShttps://soulofmathematics.comRajarshi Deyhttps://soulofmathematics.com/index.php/author/rajarshidey1729gmail-com/rich600338<blockquote class="wp-embedded-content" data-secret="YQtF0FT2CN"><a href="https://soulofmathematics.com/index.php/chaos-theory/">CHAOS THEORY</a></blockquote><iframe sandbox="allow-scripts" security="restricted" src="https://soulofmathematics.com/index.php/chaos-theory/embed/#?secret=YQtF0FT2CN" width="600" height="338" title="“CHAOS THEORY” — SOUL OF MATHEMATICS" data-secret="YQtF0FT2CN" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe><script type="text/javascript"> /* <![CDATA[ */ /*! This file is auto-generated */ !function(d,l){"use strict";l.querySelector&&d.addEventListener&&"undefined"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!/[^a-zA-Z0-9]/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret="'+t.secret+'"]'),o=l.querySelectorAll('blockquote[data-secret="'+t.secret+'"]'),c=new RegExp("^https?:$","i"),i=0;i<o.length;i++)o[i].style.display="none";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute("style"),"height"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):"link"===t.message&&(r=new URL(s.getAttribute("src")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener("message",d.wp.receiveEmbedMessage,!1),l.addEventListener("DOMContentLoaded",function(){for(var e,t,s=l.querySelectorAll("iframe.wp-embedded-content"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute("data-secret"))||(t=Math.random().toString(36).substring(2,12),e.src+="#?secret="+t,e.setAttribute("data-secret",t)),e.contentWindow.postMessage({message:"ready",secret:t},"*")},!1)))}(window,document); /* ]]> */ </script> https://i0.wp.com/soulofmathematics.com/wp-content/uploads/2020/10/O8Bm.gif?fit=250%2C188&ssl=1250188Chaos theory is a branch of mathematics focusing on the study of chaos states of dynamical systems whose apparently random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. When employing mathematical theorems, one should remain careful about whether their hypotheses are valid within the frame of the questions considered. Among such hypotheses in the domain of dynamics, a central one is the continuity of time and space (that an infinity of points exists between two points). This hypothesis, for example, may be invalid In the cognitive neurosciences of perception, where a finite time threshold often needs to be considered. The golden age of chaos theory Felgenbaum and the logistic map Mitchell Jay Feigenbaum proposed the scenario called period doubling to describe the transition between a regular dynamics and chaos. His proposal was based on the logistic map introduced by the biologist Robert M. May in 1976. While so far there have been no equations this text, I will make an exception to the rule of explaining physics without writing equations, and give here a rather simple example. The logistic map is a function of the segment [0,1] within itself defined by: xn+1=rxn(1-xn) where n = 0, 1, … describes the discrete time, the single dynamical variable, and 0≤r≤4 is a parameter. The dynamic of this function presents very different behaviors depending on the value of the parameter r: For 0≤r≤3, the system has a fixed point attractor that becomes unstable when r=3. Pour 3<r<3,57…, the function has a periodic orbit as attractor, of a period of 2n where n is an integer that tends towards infinity when r tends towards 3,57… When r=3,57…, the function then has a Feigenbaum fractal attractor. When over the value of r=4, the function goes out of the interval [0,1] COURTESY- Christian Oestreicher, Department of Public Education, State of Geneva, Switzerland;* E-mail:hc.eg.ude@rehciertseo.naitsirhc