Two-dimensional non-autonomous neuron model with parameter-controlled multi-scroll chaotic attractors

Bao, Han; Ding, Ruoyu; Chen, Bei; Xu, Quan; Bao, Bocheng

doi:10.1016/j.chaos.2023.113228

Cited by 31 publications

(6 citation statements)

References 52 publications

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“…Hu et al 29 also discovered a multi-scroll chaotic sea in a simple sine function nonlinear 3D Sprott-A system, while a numerical and experimental validation of an improved Jerk hyperchaotic multi-scroll system has been reported with infinite number of equilibrium 28 . Systems without equilibrium, hidden attractors that exhibits multi-scroll and multi-wings has also been discovered in the Lorenz-like system with a designed saw tooth wave function 4D system using a state feedback controller 30 .…”

Section: Introductionmentioning

confidence: 96%

Robust multiple-scroll dynamics in memristive-based generator system

Adelakun

Odusote

2023

Sci Rep

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In-depth analysis of a novel multiple scroll memristive-based hyperchaotic system with no equilibrium is provided in this work. We identify a family of more complicated $$n\mathrm{th}$$ n th -order multiple scroll hidden attractors for a unique, enhanced 4-dimensional Sprott-A system. The system is particularly sensitive to initial conditions with coexistence and multistability of attractors when changing the associated parameters and the finite transient simulation time. The complexity (CO), spectral entropy (SE) algorithms, and 0-1 complexity characteristics was thoroughly discussed. On the other hand, the outcomes of the electronic simulation are validated by theoretical calculations and numerical simulations.

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Section: Introductionmentioning

confidence: 96%

Robust multiple-scroll dynamics in memristive-based generator system

Adelakun

Odusote

2023

Sci Rep

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“…Early studies primarily focused on low-dimensional chaotic systems, such as two-dimensional or threedimensional chaotic systems, with relatively simple dynamical behaviors. However, in recent years, as research has advanced, the field of chaotic systems has become more extensive and diverse, with a shift in focus towards complex chaotic systems including memristor chaotic circuits [4], multi-vortex chaotic systems [5,6], multiwing chaotic systems, and neural networks [7],where the chaotic attractor can also control the alteration of the heat conduction mechanism of the light to the cell [8]. These complex chaotic systems also exhibit richer dynamical behaviors.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Zhang,

Bi,

Guo

et al. 2024

Phys. Scr.

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This paper proposes a fourth-order double-wing chaotic system with high complexity. After conducting a dynamic analysis, it is found that the system exhibits transient chaos and a rare inverse period-doubling bifurcation phenomenon in the bifurcation diagram. The system also exhibits attractor coexistence, with periodic, quasi-periodic, indicating high sensitivity to initial values. These phenomena sufficiently demonstrate the rich dynamical characteristics of chaotic systems. By introducing an impulse function with a cosine function in the foundation of the proposed system, it is found that controllable wing number and staircase burst oscillations occur. Furthermore, the number of wings and oscillation periods vary with changes in parameters, which has significant implications in engineering applications. The circuit design and construction are carried out using the Multisim simulation software, and the digital circuit is realized by using a Field-Programmable Gate Array (FPGA). It is found that the simulation results and the actual implementation results are highly consistent with the phase portrait of the system, thus demonstrating the feasibility of the circuit. Finally, by combining the proposed system with a DNA encryption algorithm, a novel image encryption algorithm with multiple layers of encryption is designed, greatly enhancing the security of encrypted images. The security of this encryption algorithm is analyzed in terms of information entropy, key space, correlation, and resistance to attacks. It is found that the proposed encryption algorithm exhibits high confidentiality and resistance to attacks. The proposed system has significant reference value in secure communication when applied to image encryption.

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“…In computational neuroscience, therefore, several research studies have been carried out to improve our knowledge to the electrical activity of coupled neurons models [3] [3][4][5]. As a result, several phenomena were observed in those works, including firing activity [6,7], multi-scroll dynamics [8][9][10], and multistability [11][12][13]. The design of simple chaotic models with complex chaotic orbits and multiple coexistence of attractors is still a hot topic in nonlinear dynamics area [14,15].…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

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This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

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Two-dimensional non-autonomous neuron model with parameter-controlled multi-scroll chaotic attractors

Cited by 31 publications

References 52 publications

Robust multiple-scroll dynamics in memristive-based generator system

Robust multiple-scroll dynamics in memristive-based generator system

Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

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