Nonlinear behavior of a novel chaotic jerk system: antimonotonicity, crises, and multiple coexisting attractors

Kengne, Jacques; Signing, V. R. Folifack; Chedjou, Jean Chamberlain; Leutcho, Gervais Dolvis

doi:10.1007/s40435-017-0318-6

Cited by 57 publications

(21 citation statements)

References 55 publications

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“…Multistability has been previously revealed in many dynamical systems [ 29 – 34 ], including jerk systems with self-excited attractors [ 30 , 33 , 34 ] and hidden attractors [ 3 , 6 , 35 ]. But the models presented up to date achieved at most six coexisting attractors in the phase space.…”

Section: System's Dynamicsmentioning

confidence: 99%

A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

Tsafack

Kengne

2018

The Scientific World Journal

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A novel autonomous 5-D hyperjerk RC circuit with hyperbolic sine function is proposed in this paper. Compared to some existing 5-D systems like the 5-D Sprott B system, the 5-D Lorentz, and the Lorentz-like systems, the new system is the simplest 5-D system with complex dynamics reported to date. Its simplicity mainly relies on its nonlinear part which is synthetized using only two semiconductor diodes. The system displays only one equilibrium point and can exhibit both periodic and chaotic dynamical behavior. The complex dynamics of the system is investigated by means of bifurcation analysis. In particular, the striking phenomenon of multistability is revealed showing up to seven coexisting attractors in phase space depending solely on the system's initial state. To the best of author's knowledge, this rich dynamics has not yet been revealed in any 5-D dynamical system in general or particularly in any hyperjerk system. Pspice circuit simulations are performed to verify theoretical/numerical analysis.

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Section: System's Dynamicsmentioning

confidence: 99%

A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

Tsafack

Kengne

2018

The Scientific World Journal

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“…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

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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.

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“…We can mention the Rossler system [2], Chen system [3], Jafari system [4], Pham system [5], and Lü system just to name a few [6]. In the last few years, special attention has been given to "jerk systems" because of their simplicity and complex dynamics [7][8][9][10][11][12]. From a mathematical point of view, a generalization of the jerk dynamics is usually given in the following form:…”

Section: Introductionmentioning

confidence: 99%

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

et al. 2020

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In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic attractors and stable fixed points. The dynamic properties of the new system are explored in terms of equilibrium point analyses, symmetry and dissipation, and existence of attractors as well. Common analysis tools (i.e., bifurcation diagram, Lyapunov exponents, and phase portraits) are used to highlight some important phenomena such as period-doubling bifurcation, chaos, periodic windows, and symmetric restoring crises. More interestingly, the system under consideration shows the coexistence of several types of stable states, including the coexistence of two, three, four, six, eight, and ten coexisting attractors. In addition, the system is shown to display antimonotonicity and offset boosting. Laboratory experimental measurements show a very good coherence with the theoretical predictions.

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Nonlinear behavior of a novel chaotic jerk system: antimonotonicity, crises, and multiple coexisting attractors

Cited by 57 publications

References 55 publications

A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

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

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

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