Multiscroll in Coupled Double Scroll Type Oscillators

Dana, Syamal K.; Singh, Bhavna; Chakraborty, Satyabrata; Yadav, Ram Chandra; Kurths, Jüergen; Osipov, Grigory V.; Roy, Prodyot Kumar; Hu, Chin‐Kun

doi:10.1142/s0218127408022196

Cited by 17 publications

(10 citation statements)

References 21 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, some of them do have partial analytical solutions [1][2][3][4][5][6][7][8][9][10][11]. For instance [3] is a seminal paper on continuous time multi-scroll attractors, and it is a generalization of the Chua's circuit.…”

Section: Introductionmentioning

confidence: 99%

Integrated circuit generating 3- and 5-scroll attractors

Trejo-Guerra

Tlelo‐Cuautle

Jiménez-Fuentes³

et al. 2012

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Integrated circuit generating 3- and 5-scroll attractors

Trejo-Guerra

Tlelo‐Cuautle

Jiménez-Fuentes³

et al. 2012

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…This task was accomplished by means of the evaluation of the Lyapunov spectrum using a method developed to overcome the drawbacks underlying this model 48 without the need to apply methodologies based on time series analysis or laborious partition of the phase space for obtaining the variational equation in the tangent map approach. 37,38,42,50 It is also important to emphasize that there are different ways of generating multiscroll attractors, 12,14,28,33 being a general approach to analyse all of them virtually impossible. For instance, in Dana et al, 14 the multiscroll structure is generated by specific couplings of dynamical systems originally operating in different steady states.…”

Section: Discussionmentioning

confidence: 99%

“…37,38,42,50 It is also important to emphasize that there are different ways of generating multiscroll attractors, 12,14,28,33 being a general approach to analyse all of them virtually impossible. For instance, in Dana et al, 14 the multiscroll structure is generated by specific couplings of dynamical systems originally operating in different steady states. This outlines a scenario not suitable for the performed analysis, as shown, for instance, in Fig.…”

Section: Discussionmentioning

confidence: 99%

Characterization of multiscroll attractors using Lyapunov exponents and Lagrangian coherent structures

Fazanaro

Soriano

Suyama

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

The present work aims to apply a recently proposed method for estimating Lyapunov exponents to characterize-with the aid of the metric entropy and the fractal dimension-the degree of information and the topological structure associated with multiscroll attractors. In particular, the employed methodology offers the possibility of obtaining the whole Lyapunov spectrum directly from the state equations without employing any linearization procedure or time series-based analysis. As a main result, the predictability and the complexity associated with the phase trajectory were quantified as the number of scrolls are progressively increased for a particular piecewise linear model. In general, it is shown here that the trajectory tends to increase its complexity and unpredictability following an exponential behaviour with the addition of scrolls towards to an upper bound limit, except for some degenerated situations where a non-uniform grid of scrolls is attained. Moreover, the approach employed here also provides an easy way for estimating the finite time Lyapunov exponents of the dynamics and, consequently, the Lagrangian coherent structures for the vector field. These structures are particularly important to understand the stretching/folding behaviour underlying the chaotic multiscroll structure and can provide a better insight of phase space partition and exploration as new scrolls are progressively added to the attractor.

show abstract

“…The design of simple chaotic models with complex chaotic orbits and multiple coexistence of attractors is still a hot topic in nonlinear dynamics area [14,15]. Many research works have been focused on the enhancement of the complexity of chaotic sequences by designing n-scroll chaotic systems using generalized multi-breakpoint piecewise linear functions in existing circuits [8,[16][17][18]. Ning et al proposed an emerging multi-double-scroll attractor via simplified piecewise-linear Chua's diode and generate up to ten-double-scroll [6].This complexity is reflected in the fact that the phase trajectory of the chaotic attractor can randomly jump between different scrolls, thereby becoming highly unpredictable [19].…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

show abstract

Multiscroll in Coupled Double Scroll Type Oscillators

Cited by 17 publications

References 21 publications

Integrated circuit generating 3- and 5-scroll attractors

Integrated circuit generating 3- and 5-scroll attractors

Characterization of multiscroll attractors using Lyapunov exponents and Lagrangian coherent structures

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Contact Info

Product

Resources

About