Dynamics, control and symmetry-breaking aspects of a new chaotic Jerk system and its circuit implementation

Kengne, Léandre Kamdjeu; Kamdem, Hervé Thierry Tagne; Pone, Justin Roger Mboupda; Kengne, Jacques

doi:10.1140/epjp/s13360-020-00338-3

Cited by 19 publications

(8 citation statements)

References 50 publications

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“…In order to investigate the MI phenomenon in BECs under consideration and build the exact analytical soliton-like solutions of equation (1) with potential (2), we employ the similarity transformation technique, a method often applied to obtain the analytical solutions in nonlinear optics [44,[55][56][57][58]. Motivated by the well-known lens transformation for the NLS equation [59], we introduce, for investigating the MI related properties in this case, the suitable ansatz…”

Section: Modulation Instability Phenomenon In Becs With Two-and Three...mentioning

confidence: 99%

“…Therefore, the investigation for nonlinear differential equations of Schrödinger-type with distributed coefficients and external potential is significant. Nonlinear partial differential equations of Schrödinger-type are fundamental nonlinear models which have been widely applied in quantum physics, optical fiber, nonlinear transmission networks, and fluid system [43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

“…∂ 2 ψ ∂x 2 + g|ψ| 2 ψ + Γ|ψ| 4 ψ + V(x, t)ψ, (1) with potential V(x, t) given as [44] V(x, t) = k(t)x 2 + λ(t)x + iγ(t), (2) where the temporal and spatial coordinates t and x are measured in units of 1/ω ⊥ and a ⊥ , respectively. Here, a ⊥ = /(mω ⊥ ) and a 0 = /(mω 0 ) are linear oscillator lengths in the transverse and cigar-axis directions, respectively; ω ⊥ and ω 0 are the corresponding harmonic-oscillator frequencies, while m is the atomic mass.…”

Section: Introductionmentioning

confidence: 99%

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Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients*

Kengne

Liu

2020

J. Phys. B: At. Mol. Opt. Phys.

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In this work, we consider the generalized cubic–quintic dissipative Gross–Pitaevskii equation, which governs the dynamics of matter wave solitons in Bose–Einstein condensates with two- and three-body interatomic interactions in a spatiotemporal-dependent dissipative potential consisting of parabolic, linear, and complex terms. By using the ansatz method, the modulational instability and gray, kink, and bright soliton solutions are presented under certain parametric conditions. We found that the complex potential, related to the feeding or the loss of atoms by the condensates seriously modifies the instability and stability domain, while the linear potential has not effect on the stability of the system. With the use of exact analytical soliton-like solutions, we investigate analytically the solitons control system, and the results show that the soliton control system may relax the limitations to parametric conditions. We found that the motion of matter wave solitons in the systems can be manipulated by controlling both the external harmonic and linear trapping potentials. We have established that the amplitude of the matter wave solitons keep no change in propagating in the system though the total number of the condensate atoms decreases (increases) when the condensate losses (gains) atoms. We also showed that the three-body interatomic interactions is responsible of the soliton compression. Our results also revealed that the found exact soliton-like solutions can be used to describe the compression of matter wave solitons in BEC system with loss of atoms.

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Section: Modulation Instability Phenomenon In Becs With Two-and Three...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients*

Kengne

Liu

2020

J. Phys. B: At. Mol. Opt. Phys.

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“…Where a b , are positive constants. With reference to the chaotic system construction method in the literature [28], a new four-dimensional memristor-based chaotic system is designed by introducing the equation (1) into the Jerk system reported in the literature [29], which has the following mathematical expression = = + = ---=…”

Section: Introductionmentioning

confidence: 99%

A new memristor-based fractional-order chaotic system

Peng

Leng

et al. 2021

Phys. Scr.

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In this paper, a new four-dimensional incommensurate fractional-order system is proposed by introducing an ideal flux-controlled memristor into a three-dimensional chaotic system, and combining it with fractional-order calculus theory, which is solved by using the Adomian decomposition method (ADM). Through theoretical analysis we found the system has numerous equilibrium points. Compared with the original system, the modified system exhibits richer dynamical behaviors. The main manifestations are: (i) Antimonotonicity varying with the initial value.(ii) Three kinds of transient transition behaviors: transient asymptotically-period (A-period), transient chaos, and tri-state transition (chaos-A-period-chaos). (iii) Initial offset boosting behavior. (iv) Hidden extreme multistability. (v) As the order q changes, the system is capable of generating a variety of asymptotically periodic attractors and chaotic attractors. These behaviors above are analyzed in detail by means of numerical simulations such as phase diagram, bifurcation diagram, Lyapunov exponent spectrum (LEs), time-series diagram, and attraction basin. Finally, the system is implemented with a hardware circuit based on a digital signal processor (DSP), which in turn proved the correctness of the numerical analysis simulations and the physical realizability of the system.

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“…[ 16,21–23 ] During the past 2 decades, many powerful and efficient methods have been developed by diverse researchers to investigate, through exact solutions of nonlinear evolution equations, the dynamics of modulated waves in NLTNs with or without dissipation. [ 23–30 ] Using nonlinear Schrö dinger equation as the model equation for slowly modulated waves propagating in NLTNs, some interesting nonlinear phenomena of NLTNs have been discovered, such as modulation instability, solitons, and rogue waves (RWs). [ 20,29,31–36 ] In recent decades, these nonlinear phenomena have undergone much theoretical and experimental research.…”

Section: Introductionmentioning

confidence: 99%

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

Kengne

Liu

2021

Advcd Theory and Sims

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A discrete nonlinear transmission network with dispersive element is considered. It is shown that the dynamics of slowly modulated waves propagating in this network are governed by a generalized cubic‐quintic nonlinear Schrödinger equation with self‐steepening and self‐frequency shift. Through the baseband modulational instability (MI) analysis, the conditions for this network to support the propagation of chirped super rogue waves (SRWs) are obtained. Based on the analytical rational solutions of the governed equation, chirped first‐ and second‐order super rogue waves are engineered in the nonlinear transmission network under consideration. The effects of the dispersive elements of the network on the chirped SRWs propagating in the network system are investigated. Particularly, it is shown that the introduction of the dispersive linear capacitance of the network enhances the baseband MI and both the derived SRWs and the corresponding frequency chirp are localized in both time and space. It is also shown that the structure of the frequency chirp depends strongly on the pulse self‐steepening and self‐frequency shift.

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Dynamics, control and symmetry-breaking aspects of a new chaotic Jerk system and its circuit implementation

Cited by 19 publications

References 50 publications

Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients*

Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients*

A new memristor-based fractional-order chaotic system

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

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