Reversal of period doubling, multistability and symmetry breaking aspects for a system composed of a van der pol oscillator coupled to a duffing oscillator

Ramadoss, Janarthanan; Kengne, Jacques; Tanekou, Sosthene Tsamene; Rajagopal, Karthikeyan; Kenmoé, G. Djuidjé

doi:10.1016/j.chaos.2022.112157

Cited by 18 publications

(8 citation statements)

References 33 publications

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“…Coexisting attractors refer to the existence of multiple attractors within a system under a set of initial values [20][21][22][23]. By setting the parameters and altering only the initial conditions, the system's trajectory converges to different states, including stable points, periodic orbits, chaos, and even hyperchaos [24].…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

Zhu,

Bai,

Dong

2024

Phys. Scr.

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A novel two-memristor hyperchaotic system is obtained by introducing a cubic magnetic-controlled memristor and a hyperbolic sine function memristor. The dynamics of the new system are analyzed by various techniques such as Lyapunov exponents, complexity, 0-1 test, bifurcation diagram and phase diagram. The results demonstrate that the new system exhibits complex dynamic behaviors, including transient chaos, transient transition, intermittent chaos, and offset-boosting. Notably, a rare phenomenon with stable unfixed point has been discovered in this newly proposed system. The largest Lyapunov exponent of the stable unfixed point fluctuates around 0 and remains predominantly less than or equal to 0. Despite this, the new system still partially exhibits chaotic characteristics, indicating that the stable unfixed point can be regarded as a local chaotic attractor. Furthermore, there are four types of coexisting attractors with period-period, chaos-chaos, chaos-stable unfixed point and stable unfixed point-stable unfixed point in the new system. The circuit design is implemented to validate the accuracy of the memristive chaotic system, and the consistency between numerical calculations and simulation results is confirmed. Finally, the coupling synchronization and tracking synchronization methods are designed, which hold practical applications in the field of secure communication, control systems and signal processing.

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

Zhu,

Bai,

Dong

2024

Phys. Scr.

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“…Also, Van der Pol Oscillator [17] is a classical oscillator with nonlinear damping, which exhibits a limit circle [18]. Even some recent studies concentrate on dynamics of Van der Pol oscillator, such as its complex bifurcation and hysteresis [19], multistability and symmetry breaking coupled to a Duffing oscillator [20], antimonotonicity and coexisting attractors under the inclusion of an active RC section [21] and so on. As a classical model of cylindrical system, mathematical pendulum also has attracted much attention for a long time.…”

Section: Introductionmentioning

confidence: 99%

The complicated dynamical behaviours of a geometrical oscillator with a mass parameter

Huang

Cao

2023

Preprint

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In this paper, we consider a special kind of geometrical nonlinear oscillator with a mass parameter admitting two different dynamical states leading to a double-valued potential energy. A cylindrical manifold is introduced to formulate the equation of motion to describe the distinguished dynamical behaviours. With the help of Hamiltonian, the complex bifurcations are demonstrated with the varying of parameters including periodic solutions, the steady states and the blowing up phenomenon near θ = ± π/2 to infinity. A toroidal manifold is introduced to map the infinities into (0, ±2, 0) on the torus exhibiting saddle-node-like behaviour, where the uniqueness of solution is failed, for which a special ‘collision’ parameter is introduced to define the possible motion leaving from the infinities. A numerical method which is proposed to get solution near the infinity where Runge-Kutta method fails, is employed to get the bifurcation diagrams using Poincaré sections for the perturbed system to exhibit the complex dynamics including the co-existence of periodic solutions, the chaos from the coexisted periodic doubling and also the instant chaos from the coexisted periodic solutions. The results demonstrated herein this paper provide a brand new insight into the understanding of enriched nonlinear dynamics and an essential explanation about ‘collision’ of mechanical system with both the geometrical and mass parameters.

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“…Few years later, Sanchez et al approaches the numerical computations of a couple Duffing's oscillator [14]. Recently, Ramadoss and co-authors coupled a Duffing oscillator with Van Der Pol oscillator and analyzed the dynamics to reveal multistabilty [15]. None of the above-mentioned works has investigated in depth the dynamics of Duffing oscillator and found some cryptographic applications.…”

Section: Introductionmentioning

confidence: 99%

Novel Duffing chaotic oscillator and its application to privacy data protection

Nkapkop

Jiang

et al. 2023

Phys. Scr.

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Traditional Compressive Sensing (CS) achieves both compression and encryption of digital data. However, most existing compressive sensing methods present some shortcomings, including weak resistance to chosen-plaintext attacks and heavy key management burden. To overcome these shortcomings, this work presents a new combination of CS with optical transformation for digital image compression and encryption. The proposed compression-encryption scheme utilizes the interesting properties of CS and permutation-diffusion techniques to reduce the image size and encrypt the image data. A novel Duffing Oscillator (NDO) is proposed, its dynamics is deeply analyzed, and its sequences are exploited to build a hardware-friendly measurement matrix for the CS process. This also contributes to reducing the total size of secret key sent to the receiving end. In addition, the final image compression-encryption output is obtained by applying one of the most significant optical encryption methods, namely Double Random Phase Encoding (DRPE). This contributes to further strengthen the security of the proposed scheme. Eventually, the experimental results imply that our scheme is effective in improving the resistance against various attacks, while guaranteeing good imperceptibility and reconstruction performance. It can then be employed in the information security communication field. Keywords: Privacy data protection, duffing oscillator, compressive sensing, double random phase encoding, security analysis.

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Reversal of period doubling, multistability and symmetry breaking aspects for a system composed of a van der pol oscillator coupled to a duffing oscillator

Cited by 18 publications

References 33 publications

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

The complicated dynamical behaviours of a geometrical oscillator with a mass parameter

Novel Duffing chaotic oscillator and its application to privacy data protection

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