Volume 17, Issue 1 -

This article analyses the basic sources and types of economic complexity: chaotic attractors and repellers, complexity catastrophes, coexistence of attractors, sensitive dependence on parameters, final state sensitivity, effects of fractal basin boundaries and chaotic saddles. Four nonlinear classic models have been used for this purpose: virtual duopoly model, model of a centrally planned economy, cobweb model with adaptive expectations and the business cycle model. The issue of economic complexity has not been sufficiently dealt with in the literature. Studies of complexity in economics usually focus on identifying the conditions under which deterministic chaos emerges in models as the main form of complexity, while analyses of other forms of complexity are much less frequent. The article has two objectives: methodological and explicative, which are to shed some new light on the issue. The first objective is to make as comprehensive a catalogue of sources of economic complexity as possible; this is to be achieved by the numerical calculations presented in this article. The issue of accumulation of complexity has been emphasized, which is a type of system dynamics which has its roots in coincidence and overlapping of complexity originating in different sources. The second objective involves an explanation of the role which is played in generating complexity by classic laws of economics. It appears that there is another overarching law, which is independent of the type of system or the level of economic analysis, which states that the long-term effect of conventional economic laws is an inevitable increase in the complexity of markets and economies. Therefore, the sources of complexity discussed in this article are called fundamental ones.

The carbuncle phenomenon, commonly occurring in solutions of compressible Euler equations, is a numerical instability associated with shock-induced anomalies. It is associated with several shock-capturing finite-volume methods designed to preserve the contact discontinuities. Due to the lack of theoretical knowledge of the carbuncle phenomenon, it is not known which numerical scheme is affected or under what circumstances that the phenomenon occur. The objective of this article is to study the numerical instability of advection upstream splitting method (AUSM) family schemes so called the AUSMD, AUSMV and AUSMDV schemes in two-dimensional structured triangular grids by examining the shock-induced anomalies produced by these original schemes in different test cases. A multidimensional dissipation technique is proposed for these schemes. The evolution of perturbations is also studied by means of a linearized discrete analysis to the odd–even decoupling problem. The recursive equations show that the AUSMDV-family schemes with the dissipation technique are less sensitive to these anomalies than the original schemes. Finally, the dissipation technique is extended to the second-order schemes and tested by several test cases.

This paper addresses the steady-state periodic and quasi-periodic responses of van der Pol–Mathieu system subject to three excitations (i.e., self, parametric and external excitations). Method of multiple scales and double perturbation technique are employed to study the original system. The cases of van der Pol–Mathieu oscillator with and without external excitation are considered, and periodic and quasi-periodic solutions are obtained and discussed. In the parametric study, the effects of various parameters and self, parametric and external excitations on the system behaviors are studied. Results from method of multiple scales well agree with those from numerical method.

This article presents the design of optimized fuzzy logic-based power system stabilizer (FPSS) to enhance small signal stability using bat algorithm (BA). The proposed optimization of scaling factors of FPSS is considered with an objective function based on square error minimization to guarantee the stability of nonlinear models of test system using BA. The BA-optimized FPSS (BAFPSS) controller is applied to the standard IEEE ten-machine thirty-nine-bus test power system model in the decentralized manner, and the performance is compared with the robust fuzzy controller. The robustness is tested by considering four different models of the test power system with different fault locations to establish the superiority of the proposed BAFPSS over the FPSS.

This paper presents an analytical solution for electrothermoelastic behavior of FGPM (functionally graded piezoelectric material) cylindrical shell. The cylindrical shell is assumed to be made up of two piezoelectric materials with their volume fractures varying along the thickness according to a simple power law. Based on classical thin shell theory, an analytical solution for electrothermoelastic performance of the FGPM cylindrical shell is presented. To investigate the influence of the power lower exponent, thermal environment, mechanical loading and electric boundary conditions on the electrothermoelastic behavior of FGPM cylindrical shells, numerical examples are presented and discussed, and some meaningful and valuable results are discovered, which will be very helpful for the design and application of such smart sensory structures.

Based on the Bernoulli–Euler beam theory, the nonlinear governing differential equations (GDEs) for a spatially deflected beam with circular cross-section are formulated, which are then reduced to first-order differential equations to be compatible with Runge–Kutta method. With the boundary conditions of a spatial beam, the governing equations are treated as an initial value problem (IVP) of ordinary differential equations. A Runge–Kutta method combined with an unconstrained optimization algorithm (RKUO) is presented to solve the IVP. The approach for determining the orientation of the cross-section plane at any position on the deflected beam is also provided. Finally, the comparison between the RKUO results and those achieved using nonlinear finite element (NFE) analysis and spatial pseudo-rigid-body model validate the accuracy and effectiveness of RKUO. The results also demonstrated the unique capabilities of RKUO to solve large spatial deflection problems that are outside the range of nonlinear finite element model.