Analysis and implementation of simple four-dimensional memristive chaotic system with infinite coexisting attractors

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Abstract

Using memristors to construct special chaotic systems is highly interesting and meaningful. A simple four-dimensional memristive chaotic system with an infinite number of coexisting attractors is proposed in this paper, which has a relatively simple form but demonstrates complex dynamical behavior. Here, we use digital simulations to further investigate the system and utilize the bifurcation diagrams to describe the evolution of the dynamical behavior of the system with the influence of parameters. We find that the system can generate an abundance of chaotic and periodic attractors under different parameters. The amplitudes of the oscillations of the state variables of the system are closely dependent on the initial values. In addition, the experimental results of the circuit are consistent with the digital simulations, proving the existence and feasibility of this memristive chaotic system.

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Authors and contacts

Corresponding author:Lai Qiang,laiqiang87@126.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 61961019), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20202ACBL212003), and the Natural Science Foundation of Hubei Province, China (Grant No. 2020CFB546).

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系统	原系统编号	原系统中非线性项的个数	新系统的总项数	新系统中非线性项的个数	文献编号
系统A	VB2	1	6	4	[22]
系统B	VB18	2	7	5	[23]
系统C	VB5	3	8	8	[24]
本系统	VB3	1	7	2	—

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参数$ a $的取值	吸引子类型	图像编号
0.1	周期-1
0.15	周期–2	图4(a)—(c)
0.155	周期–4
0.2	混沌
1.6	混沌	图4(d)—图4(f)
9.1	混沌

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系统参数	初始值	吸引子类型	图像编号
a= 1.6,b= 0.5, p= 0.2,q= 0.1	[0.1 0.1 0.2 0.5], [0.1 6.7 0.2 0.5] [0.1 6.9 0.2 0.5], [0.1 1.5 0.2 0.5] [0.1 6.5 0.2 0.5], [0.1 6.8 0.2 0.5]	三个混沌吸引子与三个周期吸引子	图7(a)
a= 0.2,b= 0.5, p= 0.2,q= 0.1	[0.1 0.1 0.2 1.2], [0.1 0.1 0.2 –0.5] [0.1 0.1 0.2 0.86], [0.1 0.1 0.2 0.5] [0.1 0.1 0.2 0.9]	三个周期吸引子与两个混沌吸引子	图7(b)
a= 6,b= 0.5, p= 0.2,q= 0.1	[0.1 0.1 0.2 0.5], [0.1 5.6 0.2 0.5] [0.1 2 0.2 0.5], [0.1 4 0.2 0.5]	两个周期吸引子与两个混沌吸引子	图7(c)
a= 8,b= 0.5, p= 0.2,q= 0.1	[0.1 –6 0.2 0.5], [0.1 6 0.2 0.5] [0.1 4 0.2 0.5], [0.1 3 0.2 0.5]	三个周期吸引子与一个混沌吸引子	图7(d)
a= 2,b= 0.6, p= 0.5,q= 0.1	[0.1 1 –0.2 1], [0.1 1 –0.2 –2] [0.1 1 –0.2 –1.2]	三个混沌吸引子	图7(e)
a= 0.5,b= 0.5, p= 0.5,q= 0.1	[0.1, 4, 0.2, 0.5], [0.1, –1, 0.2, 0.5] [0.1, 4.3, 0.2, 0.5], [0.1, –2, 0.2, 0.5]	四个混沌吸引子	图7(f)

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Vol. 71, Issue 16 - 2022-08-20

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