Various patterns of coexisting attractors in a hyperchaotic map

Gu, Haohui; Li, Chunbiao; Li, Yongxin; Ge, Xizhai; Lei, Tengfei

doi:10.1007/s11071-022-08201-z

Cited by 39 publications

(9 citation statements)

References 32 publications

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“…In chaotic systems, these attractors suggest the potential for predictable regimes, with practical implications for forecasting and optimization. Moreover, polarity balance through trigonometric functions may induce the growth of attractors [43]. The mechanisms of underlying conditional symmetry and attractor growth are elucidated through maps.…”

Section: Coexisting Attractorsmentioning

confidence: 99%

“…Yang et al [34] combined a rotation matrix and a multilayer pulse train to generate a multi-wing chaotic attractor with a switched stable node focus and hidden attractors. Moreover, the periodicity of nonlinear trigonometric functions enable chaotic systems to have multistable states, and enrich dynamical properties, their incorporation into dynamical systems to enhance offsets boosting [42], attractor regeneration [43,44], and attractor growth [44,45]. Therefore, by exploiting the periodicity of trigonometry and the topology of rotation boundary coupled modulation (RBCM), we construct a series of coexisting attractors with symmetry and growing trend.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

Zhu,

Sun,

et al. 2024

Phys. Scr.

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To provide more complex and random chaotic maps to applications and algorithms, we propose a boundary coupled modulation (BCM) model. By introducing the rotation-matrix (ROT), the corresponding rotation boundary coupled modulation (RBCM) model are constructed, and a series of hyperchaotic maps are generated with various attractors and numerous fixed points. The shape and size of the multicavity can be adjusted by controlling the parameters. Interestingly, RBCM maps are controlled by changing rotation coefficients (Rot-C, d, e, and θ), which can rotate the attractor of the enhanced BCM at any angle and direction. RBCM maps produce a more uniform topological space, and have multiple pairs of symmetric coexisting attractors. The BCM and RBCM maps exhibit rich dynamical behaviors, high complexity, and strong randomness.To verify the engineering practicability, we apply the BCM and RBCM maps to design pseudo-random number generators (PRNG), and test it with NIST, quadrature amplitude modulation (QAM) system. Finally, the FPGA implementation of the proposed chaotic map verifies.

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Section: Coexisting Attractorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

Zhu,

Sun,

et al. 2024

Phys. Scr.

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“…Coexistence is a special phenomenon in nonlinear systems. [65,66] The phenomenon that the synchronization mode of the neural network changes as the initial value of the LADM changes is shown in Figs. 3(…”

Section: -3mentioning

confidence: 99%

Synchronization coexistence in a Rulkov neural network based on locally active discrete memristor

XiaoHua

Yang

et al. 2023

Chinese Phys. B

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At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of understanding complex dynamic phenomena. Due to the properties of memorability, nonvolatility and local activity, locally active discrete memristors (LADMs) are also suitable for simulating synapses. In this paper, we use a LADM to mimic synapses and establish a Rulkov neural network model. It is found that the change of coupling strength and the initial state of the LADM leads to multiple firing patterns of the neural network. In addition, considering the influence of neural network parameters and the initial state of the LADM, numerical analysis methods such as phase diagram and timing diagram are used to study the phase synchronization. As the system parameters and the initial states of the LADM change, the LADM coupled Rulkov neural network exhibits synchronization transition and synchronization coexistence.

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“…[7][8][9] As is widely known, a memristor is a device that describes the relationship between charge and flux. [10] Since its development by HP Laboratory in 2008, memristors have found extensive applications in neural networks, [11][12][13][14][15] image encryption, [16,17] chaotic systems, [18][19][20][21][22][23][24] and more. Due to their unique biomimetic properties, such as nanoscale size, low power consumption, and non-volatility, continuous memristors are considered the optimal choice for simulating synapses in analog form.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Ma 马,

Xiong 熊,

Li 李

et al. 2024

Chinese Phys. B

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Synaptic crosstalk is a prevalent phenomenon among neuronal synapses, playing a crucial role in the transmission of neural signals. Therefore, considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks is highly necessary. In this paper, we propose a heterogeneous discrete neural network (HDNN) consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron. These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered. The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents. It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths. Furthermore, the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated, revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

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Various patterns of coexisting attractors in a hyperchaotic map

Cited by 39 publications

References 32 publications

Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

Synchronization coexistence in a Rulkov neural network based on locally active discrete memristor

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

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