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

Fuzzy synchronization of chaotic systems with hidden attractors

Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi-Sugeno (T-S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance

Managing markets and money : issues and institutions in Dutch nineteenth-century economics

Dutch nineteenth-century economics was more modern than conventional scholarship has suggested. In a number of studies of individual economists and of the formal aspects of academia, it has been concluded that at least before 1870 there were no original contributions by Dutch economists and there was a general academic backwardness of the discipline. Here we try to examine simultaneously the issues of the day and the institutional setting of academic and political economic discourse. We concentrate upon the discussion of markets, in particular the question of free trade, and the discussion of money, in particular the problems of regulating the national debt and the currency. Our picture will be that in the new Kingdom of the Netherlands economics was embraced as the science of modernity, that very soon many courses of the subject were taught in the law faculties, and that a considerable number of university professors engaged in practical policy issues. In our opinion, there is more continuity in the economic thought of Van Hogendorp (who never held a university chair) and of Ackersdijck, Mees and Pierson than most historians of Dutch economics have perceived. The fact that the latter two have also been presidents of the central bank is significant for the importance of this institution in the history of Dutch economics. We conclude that in the first two decades of the century, the new discipline gained ground outside and inside academia. From around 1820 it was well established as a subject in the law faculties, and professors like Tydeman and Ackersdijck were seen as respected authorities in the public debate on economic issues. The year 1848 saw the acceptance of a new liberal constitution and the take-off of economics as an organised community with its own specific role in Dutch society.

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

A New 3-D Multistable Chaotic System with Line Equilibrium: Dynamic Analysis and Synchronization

This work introduces a new 3-D chaotic system with a line of equilibrium points. We carry out a detailed dynamic analysis of the proposed chaotic system with five nonlinear terms. We show that the chaotic system exhibits multistability with two coexisting chaotic attractors. We apply integral sliding mode control for the complete synchronization of the new chaotic system with itself as leader-follower systems

Sistem Chaos Model Risiko Keuangan: Analisis Dinamik

Chaos phenomena appear in dynamic, nonlinear and deterministic systems. One model that is being intensively researched is financial risk. This model has system variables such as interest rate, investment demand, and stock price index. This study shows that the new financial system has interesting characteristics including multistability equilibrium points, Lyapunov exponents and bifurcation diagrams. The results of this study use MATLAB for phase diagrams of the financial system. The Lyapunov exponent and analysis of the Bifurcation diagram have been generated showing the chaotic phenomena in the intervals 0 a 15 and 0 b 0.25. The resulting Kaplan-Yorke dimension is 2.2506. The results of this study can be used to predict financial risk chaos

Projective Synchronization of Hyperchaotic Financial Systems

Based on a special matrix structure, the projective synchronization control laws of the hyperchaotic financial systems are proposed in this paper. Put a hyperchaotic financial system as the drive system, via transformation of the system state variables, construct its response system, and then design the controller based on the special matrix structure. The given scheme is applied to achieve projective synchronization of the different hyperchaotic financial systems. Numerical experiments demonstrate the effectiveness of the method

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control

A Class of Vector Lyapunov Functions for Stability Analysis of Nonlinear Impulsive Differential Systems

A novel and effective approach to stability of the solutions of nonlinear systems with impulsive effect is considered. The investigations are carried out by means of a class of vector Lyapunov functions and differential inequalities for piecewise continuous functions. Simulation examples are given to illustrate the presented results