A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors

Leutcho, Gervais Dolvis; Kengne, Jacques

doi:10.1016/j.chaos.2018.05.017

Cited by 90 publications

(27 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Hyperchaotic dynamics of coupled systems was discussed in [12]. A chaotic system with symmetry was investigated in [13]. A piecewise linear system was studied in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

Ramesh

Rajagopal

et al. 2021

Complexity

View full text Add to dashboard Cite

In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of dynamical systems is vital. Any bifurcation can cause a huge wanted/unwanted change in the states of a system. Thus, their predictions are essential in order to be prepared for the changes. Here, the systems’ bifurcations are studied using three indicators of critical slowing down: modified autocorrelation method, modified variance method, and Lyapunov exponent. The results present the efficiency of these indicators in predicting bifurcation points.

show abstract

“…Hyperchaotic dynamics of coupled systems was discussed in [12]. A chaotic system with symmetry was investigated in [13]. A piecewise linear system was studied in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

Ramesh

Rajagopal

et al. 2021

Complexity

View full text Add to dashboard Cite

show abstract

“…Since the occurrence of chaotic behavior in the system's dynamic has always been taken into consideration, numerous investigations have been performed on particular characteristics of chaotic or nonlinear systems, and diverse systems have been introduced. In other words, some researchers have introduced multistable [6][7][8][9], megastable [10][11][12], extreme multistable [13][14][15], variable-boostable [16,17], memristor-based [18][19][20], conservative [21][22][23], multicluster [24], or any kinds of symmetrical systems [25][26][27][28]. For instance, the paper proposed by Bao et al has introduced a nonautonomous 2D neural system and has also studied the multistability of the defined model [7].…”

Section: Introductionmentioning

confidence: 99%

A New Circumscribed Self‐Excited Spherical Strange Attractor

Ramamoorthy¹,

Jamal

Hussain

et al. 2021

Complexity

View full text Add to dashboard Cite

Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.

show abstract

“…These maps have been widely studied in the last decade. Some examples are Hénon map [8], 2-D sine map [9], CNN system [10], Chen and Lee system [11], jerk system [12], Chua's system [13], and hyperjerk systems [14]. It should be mention that the stability of equilibrium points is an efficient tool to foretell the dynamic of a system.…”

Section: Introductionmentioning

confidence: 99%

A New Chaotic Map With Dynamic Analysis and Encryption Application in Internet of Health Things

Sankar²,

et al. 2020

Self Cite

View full text Add to dashboard Cite

In this paper, we report an effective cryptosystem aimed at securing the transmission of medical images in an Internet of Healthcare Things (IoHT) environment. This contribution investigates the dynamics of a 2-D trigonometric map designed using some well-known maps: Logistic-sine-cosine maps. Stability analysis reveals that the map has an infinite number of solutions. Lyapunov exponent, bifurcation diagram, and phase portrait are used to demonstrate the complex dynamic of the map. The sequences of the map are utilized to construct a robust cryptosystem. First, three sets of key streams are generated from the newly designed trigonometric map and are used jointly with the image components (R, G, B) for hamming distance calculation. The output distance-vector, corresponding to each component, is then Bit-XORed with each of the key streams. The output is saved for further processing. The decomposed components are again Bit-XORed with key streams to produce an output, which is then fed into the conditional shift algorithm. The Mandelbrot Set is used as the input to the conditional shift algorithm so that the algorithm efficiently applies confusion operation (complete shuffling of pixels). The resultant shuffled vectors are then Bit-XORed (Diffusion) with the saved outputs from the early stage, and eventually, the image vectors are combined to produce the encrypted image. Performance analyses of the proposed cryptosystem indicate high security and can be effectively incorporated in an IoHT framework for secure medical image transmission.

show abstract

A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors

Cited by 90 publications

References 76 publications

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

A New Circumscribed Self‐Excited Spherical Strange Attractor

A New Chaotic Map With Dynamic Analysis and Encryption Application in Internet of Health Things

Contact Info

Product

Resources

About