Chaos is a modern science that has changed the way scientists look to the world. It studies the behaviour of nonlinear systems according to their initial state. We can see chaotic behaviour almost everywhere. As an example, rising of cigarette smoke behaviour seems smooth at the beginning then suddenly it breaks into wild swirls. A flag moves back and forth in a chaotic way, a dripping faucet goes from a steady pattern to a random one. Chaos appears in the behaviour of the weather, the behaviour of world economics, and the behaviour of fluid turbulence. Despite the environment of the system, the behaviour follows the same newly discovered laws. The realization of chaos theory has begun to change the way we think about the future [1].
The chaos term introduced in the field of dynamics while studying the behaviour of nonlinear system that is essentially depends on its initial condition. Strogatz in his book defined the term Chaos as a periodic long-term behaviour in a deterministic system that exhibits sensitive dependence on initial conditions [2].
Logistic equation is an example of one dimensional attractor. In order for us to study complicated phenomena we have to understand higher order attractor functions. Henon attractor is an example of two-dimensional attractor. It was introduced by a theoretical astronomer Michel Henon while he was studying stars movement in space [2]. On the other hand, Lorenz system is three-dimensional system published in the Journal of
Throughout recorded history, man has sought explanations for the various phenomena that occur in every facet of nature, and when no obvious answer is forthcoming, still a theory is often proposed. These explanatory theories, often taking the form of stories or chronicles, are usually linked to some sort of mysticism or divine intervention. By ascribing that which he does not understand to the gods’ will at work, man avoids facing up to his own lack of knowledge in a given area, and also draws comfort from assuming that the universe does indeed function under the guidance of divine beings. Thus the explanatory accounts that man crafts enhance his own security, quelling the fear of chaos that
studying the individual subsystems e.g., Internet .Also in a complicated system we can predict the
Chaos theory engages with the certain physical systems, which are extremely sensitive to the changes in initial conditions. The equations describing a system are highly interdependent. Therefore, even a small change in the system can result in a large effect on the later condition of the system. Since it is impossible to measure all the initial parameters exactly, the trajectory of the system’s operation is inherently indeterminate. That is, this theory is represented by the interdependence among constituents of a system and the uncertainty of the possible conditions of its stages of development. In the highly complex interrelatedness and indeterminacy, this cosmos evolves as a self-organizing creation through “the interplay of chance and law.” In that sense, as Ilya Prigogine and Stuart Kauffman hold, our cosmos is in the continuous process of the emergence of complexity and order in nonlinear systems at the edge of chaos. The dissipations and emergences of complexity and order in nonlinear systems go on and on in this cosmos. “Every beginning is a beginning-again.”
The Bifurcation diagram also called the logistic map, shows the region of all possible values of the logistic equation. The relative simplicity of the logistic map makes it a widely used point of entry into a consideration of the concept of chaos.
“It has been said something as small as the flutter of a butterfly’s wing can ultimately cause a typhoon halfway around the world.” ~ Chaos Theory
This view was in dialectical opposition to Heraclitus of Ephesus, who argued that the world is in a constant state of flux. Heraclitus argues that there is a problem with people’s attachment to the illusion of permanence. Everything in the world will not stay the same, we can see this from the idea from Heraclitus that ‘it is not possible to step twice into the same river, according to Heraclitus, nor to touch mortal substance twice in any condition’ (Plutarch, 392B). Rivers are bodies of water that continually flows so that every second the water at a point in the river is not the same as it was before. The state of the physical world has never remained the same; mountains move over millions of years, a few billion years ago Earth could not sustain life, and even longer ago there were no solids, no liquids, only gases. Each moment can be said to die and be reborn in the next, so that change occurs every moment and it
In Steven D. Levitt and Stephen J. Dubner’s Freakonomics, they use unconventional wisdom to explain certain events. They use very solid data in order to support their conclusions about certain events. However, some of their conclusions suffer from errors in reasoning, or rather, fallacies. Although they have done several different types of fallacies, the main one they’ve done is the either-or choice.
The first term relevant to this paper is determinism. (Hard) Determinism is the philosophical idea that every action and decision a
Chaos theory is a more recently discovered organization theory. Don’t let the word chaos misdirect you in your thoughts on this theory. This theory actually believes that order can be achieved,
In 1961, computers were still infancy, and the race to the moon had just begun. Edward Lorenz one of the first proponents of chaos theory developed a weather prediction model and found out that the smallest changes at the one millionth of the decimal point can make his predictions useless, he called this result as butterfly effect. The butterfly effect is a theoretical example of chaos theory. The main premise of latter is that small changes in initial condition results in vast differences in final outcome. The term butterfly effect is a metaphorical example of a hurricane being influenced by flapping of the wings of a distant butterfly several years earlier by creating tiny changes in the atmosphere.
Deterministic analysis, much alike quantitative analysis, draws its methodologies from scientific and empirical theories that are based on physical relationships and are often conveyed with respect to time.
Therefore, Eddington claims that the directionality of time is inherently within the human awareness. Human beings are essentially rational creatures who have an inborn need to make sense of the ever-increasing disorder in the world around them. We use the constant forward linear march of time to establish order in a disordered universe in which entropy continually increases.
The system is characterized by the relationships of its components and the non-linearity that exists between these components.
the paranormal with as much respect and analysis as physics or the chaos theory."13 The
Disagreement may aid the pursuit of knowledge in the natural and human sciences because disagreement leads to new discoveries. Disagreement is about gathering reliable knowledge as well as using this newfound knowledge, and occurs when a group fails to reach a consensus over the logic of an argument. Knowledge is composed of facts, information, and skills acquired by a person through experience or education. Two areas of knowledge that are impacted by disagreement are human science and natural science. Human science is the study of human behavior and how humans gather information. Natural science is a branch of science that deals with the physical world. In order for a disagreement to occur, one must be familiar with the subject and have his or her own prediction that is different from the norm. Therefore, to advance knowledge in the areas of human and natural science, people must disagree. The roles of logic, reason, and emotion will be investigated to see how they are used to help gain new knowledge in both human and natural science.