Chaos in economics and finance

Abstract

This paper focuses on the use of dynamical chaotic systems in Economics and Finance. In these fields, researchers employ different methods from those taken by mathematicians and physicists. We discuss this point. Then, we present statistical tools and problems which are innovative and can be useful in practice to detect the existence of chaotic behavior inside real data sets.

Dynamic analysis and control of a new hyperchaotic finance system

“…Therefore, system (2) shows hyperchaotic behavior, and more basic properties and complex dynamics of the new system will be given in Sect. 3.…”

“…Chaos has received more attention due to its potential applications in physics, chemical reactor, control theory, biological networks, artificial neural networks, telecommunications and secure communications. It is well known that the economy and finance systems [1][2][3][4][5] are very complicated nonlinear systems which are concerned with people and contain many complex factors. Since the chaotic phenomenon in economics was discovered in 1985, great impact was imposed on prominent economics at present.…”

Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise

“…K= ω γ h (7) In Eqs. (6) and (7), γ is the order of the differintegration and (2N + 1) is the order of the filter.…”

“…This financial system has been taken as a representative case and fractional fuzzy control policies are formulated so that the undesirable chaotic dynamics can be suppressed. In general, for real world financial data, there can be an underlying chaotic dynamical system influenced by extraneous variables, which introduce additional noise like phenomena superimposed over this [7]. Chaos in such cases can be observed by removing the noisy component in the data.…”

“…Important theoretical and practical findings based on the application of Hopf bifurcation in chaotic financial system modelling has been investigated by researchers in [3][4][5]. Applications of non-linear dynamics and chaos in economics and finance have been documented by contemporary researchers in [6][7][8]. Control and dynamic analysis of hyper-chaotic financial system has been documented by Yu et al [9].…”