Solution and dynamics analysis of a fractional‐order hyperchaotic system

Numerical solution and chaotic behaviors of the fractional‐order simplified Lorenz hyperchaotic system are investigated in this paper. The solution of the fractional‐order hyperchaotic system is obtained by employing Adomian decomposition method. Lyapunov characteristic exponents algorithm for the fractional‐order chaotic system is designed. Dynamics of the fractional‐order hyperchaotic system are analyzed by means of bifurcation diagrams, Lyapunov characteristic exponents, C₀ complexity, and chaos diagram. It shows that this system has rich dynamical behaviors, and it is more complex when the fractional order q is small. It lays a foundation for the practical application of the fractional‐order hyperchaotic systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

A proposed discretized form of fractional‐order prey‐predator model is investigated. A sufficient condition for the solution of the discrete system to exist and to be unique is determined. Jury stability test is applied for studying stability of equilibrium points of the discretized system. Then, the effects of varying fractional order and other parameters of the systems on its dynamics are examined. The system undergoes Neimark‐Sacker and flip bifurcation under certain conditions. We observe that the model exhibits chaotic dynamics following stable states as the memory parameter α decreases and step size h increases. Theoretical results illustrate the rich dynamics and complexity of the model. Numerical simulation validates theoretical results and demonstrates the presence of rich dynamical behaviors include S‐asymptotically bounded periodic orbits, quasi‐periodicity, and chaos. The system exhibits a wide range of dynamical behaviors for fractional‐order α key parameter.     

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

This paper is devoted to investigate synchronization and antisynchronization of N‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means of the direct design method, the appropriate controllers are designed to transform the fractional‐order error dynamical system into a nonlinear system with antisymmetric structure. Thus, by using the recently established result for the Caputo fractional derivative of a quadratic function and a fractional‐order extension of the Lyapunov direct method, several stability criteria are derived to ensure the occurrence of synchronization and antisynchronization among N‐coupled fractional‐order complex chaotic systems. Moreover, numerical simulations are performed to illustrate the effectiveness of the proposed design.     

中国能源消费、碳排放与经济增长的区域差异性研究

基于1990～2010年我国30个省市面板数据,采用面板计量分析方法,考察我国源消费、碳排放与经济增长三者之间相互影响关系对空间区域的依赖性.研究结果表明:能源消费、碳排放与经济增长三者之间不仅存在着相互影响的关系,且具有显著的区域差异性.各省份的经济发展均为各地区能源消费增长的重要诱因之一,这与能源消费与经济增长具有较高关联度的结论保持一致.北京、辽宁、吉林等16个省份碳排放变化与经济增长变化之间的的弹性系数为负值,而天津等其他14个省市碳排放总量还将伴随着经济增长而增长,所以弹性系数为正值,这点隐含说明当区域经济水平较高时,该区域也将拥有更多优势条件来减低碳排放,实现碳减排最终还是需要依赖于发达的经济水平.     

北京地区经济增长与碳排放脱钩状态实证研究

通过构建经济增长与碳排放脱钩状态的Tapio分析模型,研究了北京地区1999年-2008年经济增长与碳排放的脱钩关系.分析结果表明:北京地区2001年和2002年呈现经济增长和碳排放的强脱钩,2004年为扩张性耦合,其他各段时间都属于弱脱钩状态.呈现这种状态的主要原因是北京地区以第三产业为主的产业结构,以及较高的能源效率.此外,结合中间变量分析可以得到,北京地区经济增长与碳排放的脱钩主要是经济增长与能源消费脱钩的结果,减排技术并没有发挥太大的作用.据此,提出,应加强政府的控制力度,不断加强新能源的开发,提升可再生能源的利用率,大力发展碳金融市场.     

Numerical solution of nonlinear partial quadratic integro‐differential equations of fractional order via hybrid of block‐pulse and parabolic functions

In this paper, an effective numerical approach based on a new two‐dimensional hybrid of parabolic and block‐pulse functions (2D‐PBPFs) is presented for solving nonlinear partial quadratic integro‐differential equations of fractional order. Our approach is based on 2D‐PBPFs operational matrix method together with the fractional integral operator, described in the Riemann–Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations, which greatly simplifies the problem. By using Newton's iterative method, this system is solved, and the solution of fractional nonlinear partial quadratic integro‐differential equations is achieved. Convergence analysis and an error estimate associated with the proposed method is obtained, and it is proved that the numerical convergence order of the suggested numerical method is O(h³) . The validity and applicability of the method are demonstrated by solving three numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the exact solutions much easier.     

HOW RAPID SHOULD EMISSION REDUCTION BE? A GAME‐THEORETIC APPROACH

Abstract In this paper, we search for multistage realization of international environmental agreements. To analyze countries' incentives and the results of their interactions, we mathematically represent players' strategic preferences and apply a game‐theoretic approach to make predictions about their outcomes. The initial decision on emissions reduction is determined by the Stackelberg equilibrium concept. We generalize Barrett's static “emission” model to a dynamic framework and answer the question “how rapid should the emission reduction be?” It appears that sharper abatement is desirable in the early term, which is similar to the conclusion of the Stern review. Numerical example demonstrates that abatement dynamics of the coalition and the free‐rider differ when discounting of the future payoffs increases. We show that without incentives from external organizations or governments, such pollution reduction path can actually lead to a decline in the agreement's membership size.     

Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016     

Fractional modeling and control of a complex nonlinear energy supply‐demand system

This article deals with the fractional‐order modeling of a complex four‐dimensional energy supply‐demand system (FOESDS). First, the fractional calculus techniques are adopted to describe the dynamics of the energy supply‐demand system. Then the complex behavior of the proposed fractional‐order FOESDS is studied using numerical simulations. It is shown that the FOESDS can exhibit stable, chaotic, and unstable states. When it exhibits chaos, the FOESDS's strange attractors are plotted to validate the chaotic behavior of the system. Moreover, we calculate the maximal Lyapunov exponents of the system to confirm the existence of chaos. Accordingly, to stabilize the system, a finite‐time active fractional‐order controller is proposed. The effects of model uncertainties and external disturbances are also taken into account. An estimation of the stabilization time is given. Based on the latest version of the fractional Lyapunov stability theory, the finite‐time stability and robustness of the proposed method are proved. Finally, two illustrative examples are provided to illustrate the usefulness and applicability of the proposed control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 74–86, 2015