Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness. Finally, the comparative findings are discussed

Synchronization of chaos in nonlinear finance system by means of sliding mode and passive control methods: A comparative study

In this paper, two different control methods, namely sliding mode control and passive control, are investigated for the synchronization of two identical chaotic finance systems with different initial conditions. Based on the sliding mode control theory, a sliding surface is determined. A Lyapunov function is used to prove that the passive controller provides global asymptotic stability of the system. Numerical simulations validate the synchronization of chaotic finance systems with the proposed sliding mode and passive control methods. The synchronization performance of these two methods is compared and discussed

Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos

A kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction, and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a stable periodic orbit

What´s new and useful about chaos in economic science

La complejidad es una de las propiedades características del comportamiento económico. En este trabajo se exponen los principales conceptos y técnicas de la teoría del caos, analizando las distintas áreas de la ciencia económica desde el punto de vista de la complejidad y el caos. [ABSTRACT] Complexity is one of the most important characteristic properties of the economic behaviour. The new field of knowledge called Chaotic Dynamic Economics born precisely with the objective of understanding, structuring and explaining in an endogenous way such complexity. In this paper, and after scanning the principal concepts and techniques of the chaos theory, we analyze, principally, the different areas of Economic Science from the point of view of complexity and chaos, the main and most recent researches, and the present situation about the results and possibilities of achieving an useful application of those techniques and concepts in our field

Control of a novel chaotic fractional order system using a state feedback technique

We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the Routh-Hurwitz and the Matignon stability criteria, we analyze the novel chaotic fractional order system and propose a control methodology that is better than the nonlinear counterparts available in the literature, in the sense of simplicity of implementation and analysis. A scalar control input that excites only one of the states is proposed, and sufficient conditions for the controller gain to stabilize the unstable equilibrium points derived. Numerical simulations confirm the theoretical analysis. © 2013 Elsevier Ltd. All rights reserved

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations

Essays on Macroeconomic Dynamics

This thesis deals with macroeconomic dynamics. In chapter 1, I study a one-sector growth model withendogenous discount rate of the sort proposed by citet{1}. I extendthe model into a heterogeneous agents model with respect to initialwealth, and investigate whether the wealthdistribution may converge to a degenerate distribution.I find that if an agent's decision only depends on his orher reference group and if consumption is more important indiscounting than income around the steady state, then convergence to a degenerate distributionis a unique solution. Furthermore, if an agent's decision depends on averagevariables of overall society, I find that there exists a continuumof steady states.In chapter 2, I introduce three mechanisms into otherwise standard citet{aiya94} model to generate a realisticwealth distribution. The three mechanisms include: i) a wealth-dependent shock: labor income shock is wealth-dependent;ii) misspecification: people do not take into account the dependence of the labor income process on wealth when they make consumption decisions;iii) status-seeking from some threshold: there is a direct utility gain from being wealthy.The main findings are as follows:i) Wealth-dependent labor income shock with misspecification helps to explain wealth concentration but cannot fully explain the share of the top 1\% in wealth distribution.ii) In the full model with status-seeking, the share of top 1\% becomes closer to the data.In chapter 3, I build a simple model (two-dimensional discrete dynamical system) to study the interactive dynamics of short-term nominal interest rates of the U.S. and international risk appetite.Main implications from the research are the followings: First, strong interaction between short-term nominal interest rates of the U.S. and international risk appetite can induce bifurcations of the dynamical system: stable fixed point to limit cycle and then to chaos. Second, a numerical experiment suggests two possible explanations for rising variance ratios: the reduction of random shock and the bifurcation of a dynamical system. This finding hints the potential of complexity measures (such as Lyapunov exponent and permutation entropy) as early warning signals