Chaotic Dynamics of a Simple Parametrically Driven Dissipative Circuit

Philominathan, P.; Santhiah, M.; Mohamed, I. Raja; Murali, K.; Rajasekar, S.

doi:10.1142/s0218127411029537

Cited by 11 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparing this result with Eqs. (9) and (10) we conclude that the exponent δ = −1. This finding is in good agreement with the simulations shown in Fig.…”

Section: An Analytical Description To the Equilibriummentioning

confidence: 56%

Convergence towards asymptotic state in 1-D mappings: A scaling investigation

et al. 2015

View full text Add to dashboard Cite

Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control parameter is varied bifurcations in the fixed points appear. We verified at the bifurcation point in both; the transcritical, pitchfork and period-doubling bifurcations, that the decay for the stationary point is characterized via a homogeneous function with three critical exponents depending on the nonlinearity of the mapping. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law whose slope is independent of the nonlinearity. The formalism is general and can be extended to other dissipative mappings.

show abstract

“…Comparing this result with Eqs. (9) and (10) we conclude that the exponent δ = −1. This finding is in good agreement with the simulations shown in Fig.…”

Section: An Analytical Description To the Equilibriummentioning

confidence: 56%

Convergence towards asymptotic state in 1-D mappings: A scaling investigation

et al. 2015

View full text Add to dashboard Cite

show abstract

“…In this paper we concentrate in the local bifurcations. Applications and observations of such bifurcations are wide in the literature and include laser [7][8][9] , population dynamics [10,11] , chemical reactions [12,13] , electric circuits [14,15] , discrete mappings [16,17] and many others [18][19][20][21][22] .…”

Section: Introductionmentioning

confidence: 99%

Defining universality classes for three different local bifurcations

Leonel

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

The convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations.

show abstract

“…After his publication many different contributions appeared. Applications of mappings are vast and can be seen in physics [2][3][4][5][6] , chemistry, biology, engineering, mathematics and many others [7][8][9][10][11][12][13][14][15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

Dynamics towards the steady state applied for the Smith-Slatkin mapping

Oliveira

Ramos

Leonel

2018

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

We derived explicit forms for the convergence to the steady state for a 1-D Smith-Slatkin mapping at and near at bifurcations. We used a phenomenological description with a set of scaling hypothesis leading to a homogeneous function giving a scaling law. The procedure is supported by numerical simulations and confirmed by a theoretical description. At the bifurcation we used an approximation transforming the difference equation into a differential one whose solution remount all scaling features. Near the bifurcation an investigation of fixed point stability leads to the decay for the stationary state. Simulations are made in the pitchfork, transcritical and period doubling bifurcations.

show abstract

Chaotic Dynamics of a Simple Parametrically Driven Dissipative Circuit

Cited by 11 publications

References 18 publications

Convergence towards asymptotic state in 1-D mappings: A scaling investigation

Convergence towards asymptotic state in 1-D mappings: A scaling investigation

Defining universality classes for three different local bifurcations

Dynamics towards the steady state applied for the Smith-Slatkin mapping

Contact Info

Product

Resources

About