Chaos Theory Studying and Developments

Introduction Chaos theory is a mathematical domain, with applications in various areas of study including economics, biology, philosophy, engineering and physics (Krist 12).Advertising We will write a custom research paper sample on Chaos Theory Studying and Developments specifically for you for only $16.05 $11/page Learn More Chaos theory determines inherent behaviour and characteristics of dynamical entities that are predominantly sensitive to initial conditions, an occurrence known as the butterfly effect. Any slight change in initial conditions such as errors in mathematical computation produces divergent results for such dynamical systems (Krist 14). Such a scenario makes it difficult to generate long-term predictions in general. The future of dynamical systems largely depends on initial conditions without involvement of random factors or elements (Krist 17). This makes the systems unpredictable. Such scenarios qualify as deterministic chaos. Chaoti c tendencies manifest in several natural systems. For instance, weather patterns are usually chaotic and unpredictable. For instance, mathematical model and Poincare maps help to achieve such results (Krist 23). A chaotic dynamical system must possess several characteristics. The system must conform to the reality surrounding the immediate conditions. It must integrate all topological factors and circumstances. The system must have dense periodic orbits. There must be conditions that act contrary to established original conditions. Chaos theory explains the rationale of chaotic events in the world. This theory explains why certain things happen the way they do. Discussion Henri Poincare initially proposed chaos theory in 1880s. He discovered that there were orbits that did not show consistency in their characteristic behaviour. Mathematicians formulated a large portion of this theory (Krist 27). Early theorists called it ergodic theory. Later studies centred on basic principles of p hysics. They majored on turbulence, astronomy, engineering, and tri-body problem. During early days of these studies, there was no clear understanding on the topic of inconsistent planetary movement. However, there was slight knowledge on the issue relating to turbulence in the movement of liquids (Skiadas 35). Researchers had knowledge on alternate movements in radio circuits. However, they did not have any theory to explain these occurrences. The subsequent developments presented an opportunity for them to expound on their earlier studies (Skiadas 41).Advertising Looking for research paper on philosophy? Let's see if we can help you! Get your first paper with 15% OFF Learn More The studies gained acceptance after scholars realized that linear theory could not account trends observed in various experiments (Skiadas 44). The area of study encompassed minor incidents that proved irrelevant in earlier theories. The studies accelerated with the advent of the electronic co mputer. The mathematical inferences in the theory were difficult to solve using manual procedures. Therefore, computers simplified the work involved in solving such procedures (Skiadas 44). Edward Lorenz contributed in the development of knowledge through extensive research on climatic trends and manifestations. Edward used a digital computer to simulate data. He achieved this by adding cumulative data to produce successive results (Skiadas 45). He realized that the digital computer produced varying results. He rightly attributed these results to the accuracy of the computer. However, critics argued that these inferences were minute and inconsequential. Lorenz had established relationship between minute changes and eventual outcomes. This discovery proved that atmospheric experiments lacked the capacity to generate accurate climatic predictions (Skiadas 47). Chaos theory provided a clear roadmap for understanding and determining weather patterns over certain duration. It presented p ossibilities for various forms of research and understanding on natural chaotic situations. Through it, complex situations acquired meaning and sense (Williams 63). Scientists use it to investigate natural occurrences with a view to gather inferential data that helps to derive accurate deductions. Chaos theory is useful in understanding chaotic situations that influence the quality of human existence (Williams 65). However, the initial theory could not offer conclusive solutions to natural chaotic events. It had several loopholes that increased its vulnerability to inaccuracy. It affected the quality of life and changed people’s perception on things that occurred around them (Williams 71). Chaotic tendencies manifest in various occurrences such as electric circuits, laser equipments, and fluid reactions. Natural manifestations of chaotic behaviour include weather patterns, trends in the solar system, ecological changes, and molecular activity (Williams 75). Chaos theory influ ences various areas of modern existence. For instance, it is instrumental in the ongoing research related to epilepsy. Chaos theory continues to influence various aspects in contemporary life situations. For instance, movies and literature show the influence of this development on modern life. The study of chaos theory has affected various aspects of social life. The theory has intensified the development of modern technologies that are necessary for improved and better living. Therefore, people understand various aspects that define modern living (Williams 77).Advertising We will write a custom research paper sample on Chaos Theory Studying and Developments specifically for you for only $16.05 $11/page Learn More The theory shaped lives of people during the period it conceptualized. People understood the various natural occurrences and their effects on human existence. Through this development, people directed more attention to things that seemed irrel evant. For instance, people took keen interest on minor climatic changes that manifested in daily life. Such understanding was critical for enhancing constructive discourse on matters that related to human existence (Williams 78). The theory catapulted scientific discourse to new heights. Its formulation contributed to the business success. Many business enthusiasts capitalized on its development to initiate innovative business ventures that experienced monumental and unprecedented success (Vierling 21). The contributions occasioned by the development of this theory were instrumental in determining the course of history. Subsequent scholars formulated advanced theories based on the initial principles and rationale of this theory. Various fields of study continue to draw inspiration from the basic principles of this theory. With the advent of advanced technology, society has benefited from this development. Technology enables the advanced exploitation of basic theoretical principles embodied in the theory (Vierling 24). Modern life would be different without chaos theory. It would be difficult for people to understand the events that manifest in daily life situations. Absence of this theory would affect people’s perception of natural occurrences that define daily lives in modern world (Vierling 26). For instance, it would be difficult for people to make sense of events that are beyond human understanding. Such events influence the way people conduct themselves in reaction to natural occurrences. The contributions of this area of knowledge are numerous and immeasurable (Vierling 27). Without this knowledge, the world would rank lower in areas of social and technological advancements. Conclusion It is very important that we study this theoretical discourse. By understanding it, we acquire knowledge on how minute events influence bigger events that shape modern living. By studying this theory, we fathom the various developmental stages that have shaped and determined modern technological advancements. Therefore, it consolidates various efforts that resulted into deeper understanding of natural occurrences (Vierling 34). By studying this theory, we appreciate the role of science in enhancing development and advancing favourable innovations. Chaos theory explains the rationale of chaotic events in the world. This explains why certain things happen the way they do. Developments around this area continue to influence modern trends in science and technology. The advancements of chaos theory remain a critical influence on contemporary life.Advertising Looking for research paper on philosophy? Let's see if we can help you! Get your first paper with 15% OFF Learn More Works Cited Krist, Gary. Chaos Theory. London: Jove Books, 2001. Print. Skiadas, Christos. Chaos Theory: Modelling, Simulation and Applications. London: World Scientific, 2011. Print. Vierling, Matthew. Chaos Theory: A Novel of Psychological Suspense. New York: Universal Press, 2003. Print. Williams, Garnett. Chaos Theory Tamed. London: Joseph Henry Press, 1997. Print. This research paper on Chaos Theory Studying and Developments was written and submitted by user Cl0ud9 to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.