Research Papers

Chaotic Behavior and Its Control in a Fractional-Order Energy Demand–Supply System

[+] Author and Article Information
Dongqin Chen

College of Mathematics and Statistics,
Nanjing University of Information
Science and Technology,
Nanjing 210044, China
e-mail: cdqlinsey@163.com

Wenjun Liu

College of Mathematics and Statistics,
Nanjing University of Information
Science and Technology,
Nanjing 210044, China
e-mail: wjliu@nuist.edu.cn

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 15, 2016; final manuscript received June 20, 2016; published online July 22, 2016. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 11(6), 061010 (Jul 22, 2016) (7 pages) Paper No: CND-16-1138; doi: 10.1115/1.4034048 History: Received March 15, 2016; Revised June 20, 2016

In this paper, we first propose a fractional-order energy demand–supply system, with the background of the energy resources demand in the eastern regions of China and the energy resources supply in the western regions of China. Then, we confirm the energy resource attractor with a necessary condition about the existence of chaotic behaviors. By employing an improved version of Adams Bashforth Moulton algorithm, we use three cases with different fractional values to verify the necessary condition. Finally, chaos control of fractional-order energy demand–supply system is investigated by two different control strategies: a linear feedback control and an adaptive switching control strategy via a single control input. Numerical simulations show that the energy demand and import in Eastern China and energy supply in Western China are self-feedback controlled around the system’s equilibrium point.

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Grahic Jump Location
Fig. 1

The numerical simulation result for system (4) when (q1,q2,q3)=(0.98,0.97,0.96)

Grahic Jump Location
Fig. 2

The numerical simulation result for system (4) when (q1,q2,q3)=(0.86,0.86,0.84)

Grahic Jump Location
Fig. 4

The control of chaotic energy demand–supply system (15) with (k1,k2,k3)=(−0.12,−0.02,−0.042) is stable in the equilibrium point (0.8,0.1255,0.1412)

Grahic Jump Location
Fig. 5

The control processes of energy demand–supply system’s variables

Grahic Jump Location
Fig. 3

The numerical simulation result for system (4) when (q1,q2,q3)=(0.44,0.84,0.75)

Grahic Jump Location
Fig. 6

State trajectories of the fractional-order chaotic energy demand–supply system

Grahic Jump Location
Fig. 7

Time history of the single control input in control of chaotic system

Grahic Jump Location
Fig. 8

Time response of the adaptive parameter in control of chaotic system



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