A New 3D Chaotic Attractor in Gene Regulatory Network

Kozlovska, Olga; Sadyrbaev, Felix; Samuilik, Inna

doi:10.3390/math12010100

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…After the discovery of the three-dimensional Lorenz system [10], a large number of chaotic systems were presented. Some typical systems are chaotic oscillators without equilibrium [11], with stable equilibrium [12], and with equilibrium point located on a segmented straight line [13,14]. In [15], authors investigated chaotic oscillators with balanced squares, while a chaotic oscillator with circular equilibrium was studied in [16].…”

Section: Introductionmentioning

confidence: 99%

Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications

Almatroud,

Shukur,

Pham

et al. 2024

Mathematics

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We explore an oscillator with nonlinear functions and equilibrium lines that displays chaos. The equilibrium stability and complexity of the oscillator have been analysed and investigated. The presence of multiple equilibrium lines sets it apart from previously reported oscillators. The synchronization of the oscillator is considered as an application for secure communications. An observer is designed by considering a transmitted signal as a state, in other words, by injecting a linear function satisfying Lipschitz’s condition to the proposed oscillator. Moreover, the adaptive control of the new oscillator is obtained.

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Section: Introductionmentioning

confidence: 99%

Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications

Almatroud,

Shukur,

Pham

et al. 2024

Mathematics

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Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control

Johansyah,

Sambas,

Hannachi

et al. 2024

Mathematics

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In this paper, we investigated a three-dimensional chaotic system that models key aspects of a monetary system, including interest rates, investment demand, and price levels. The proposed system is described by a set of autonomous quadratic ordinary differential equations. We analyze the dynamic behavior of this system through equilibrium points and their stability, Lyapunov exponents (LEs), and bifurcation diagrams. The system demonstrates a variety of behaviors, including chaotic, periodic, and equilibrium states depending on parameter values. Additionally, we explore the multistability of the system and present a radial basis function neural network (RBFNN) controller design to stabilize the chaotic behavior. The effectiveness of the controller is validated through numerical simulations, highlighting its potential applications in economic and financial modeling.

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A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization

Kopp,

Samuilik

2024

Chaos Theory and Applications

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This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method.

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A New 3D Chaotic Attractor in Gene Regulatory Network

Cited by 3 publications

References 31 publications

Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications

Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications

Dynamics and Stabilization of Chaotic Monetary System Using Radial Basis Function Neural Network Control

A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization

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