scholarly journals Type-II intermittency in a class of two coupled one-dimensional maps

2000 ◽  
Vol 5 (3) ◽  
pp. 233-245 ◽  
Author(s):  
J. Laugesen ◽  
E. Mosekilde ◽  
T. Bountis ◽  
S. P. Kuznetsov
Keyword(s):  
Period Doubling ◽  
Coupled System ◽  
Two Dimensions ◽  
Type Ii ◽  
One Dimensional ◽  
System A ◽  
Subcritical Hopf Bifurcation ◽  
Theoretical Predictions ◽  
The Individual ◽  
One Dimensional Maps

The paper shows how intermittency behavior of type-II can arise from the coupling of two one-dimensional maps, each exhibiting type-III intermittency. This change in dynamics occurs through the replacement of a subcritical period-doubling bifurcation in the individual map by a subcritical Hopf bifurcation in the coupled system. A variety of different parameter combinations are considered, and the statistics for the distribution of laminar phases is worked out. The results comply well with theoretical predictions. Provided that the reinjection process is reasonably uniform in two dimensions, the transition to type-II intermittency leads directly to higher order chaos. Hence, this transition represents a universal route to hyperchaos.

ROUTE TO CHAOS VIA INVERSE CASCADE OF CONTINUOUS BIFURCATIONS

1995 ◽  
Vol 05 (01) ◽  
pp. 123-132 ◽  
Author(s):  
M. GUTMAN ◽  
V. GONTAR
Keyword(s):  
Period Doubling ◽  
Scaling Behavior ◽  
One Dimensional ◽  
Inverse Cascade ◽  
Discontinuous Bifurcation ◽  
Universal Properties ◽  
Route To Chaos ◽  
Piecewise Continuous ◽  
One Dimensional Maps

A route to chaos via an inverse cascade of continuous bifurcations that arithmetically reduce the period of successive orbits has been obtained for piecewise continuous one-dimensional maps. We have studied the mechanism of these bifurcations and established that their scaling behavior is governed by constants with new universal properties. The possibility of obtaining discontinuous bifurcation from any selected orbit of a cascade of period-doubling to any orbit of inverse cascade has been demonstrated.

BIRKHOFF SPECTRA FOR ONE-DIMENSIONAL MAPS WITH SOME HYPERBOLICITY

2010 ◽  
Vol 10 (01) ◽  
pp. 53-75 ◽  
Author(s):  
YONG MOO CHUNG
Keyword(s):  
Dynamical System ◽  
Hausdorff Dimension ◽  
Multifractal Analysis ◽  
Probability Measures ◽  
One Dimensional ◽  
System A ◽  
Topologically Mixing ◽  
One Dimensional Maps ◽  
Dimension One

We study the multifractal analysis for smooth dynamical systems in dimension one. It is given a characterization of the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of hyperbolic measures for a topologically mixing C2 map modeled by an abstract dynamical system. A characterization which corresponds to above is also given for the ergodic basins of invariant probability measures. And it is shown that the complement of the set of quasi-regular points carries full Hausdorff dimension.

scholarly journals Universal Features of Tangent Bifurcation

1985 ◽  
Vol 38 (1) ◽  
pp. 1 ◽  
Author(s):  
R Delbourgo ◽  
BG Kenny
Keyword(s):  
Renormalization Group ◽  
Limit Cycles ◽  
Period Doubling ◽  
Accumulation Point ◽  
Universal Functions ◽  
One Dimensional ◽  
Chaotic Region ◽  
Renormalization Group Equations ◽  
Tangent Bifurcation ◽  
One Dimensional Maps

We exhibit certain universal characteristics of limit cycles pertaining to one-dimensional maps in the 'chaotic' region beyond the point of accumulation connected with period doubling. Universal, Feigenbaum-type numbers emerge for different sequences, such as triplication. More significantly we have established the existence of different classes of universal functions which satisfy the same renormalization group equations, with the same parameters, as the appropriate accumulation point is reached.

scholarly journals Analysis of two-dimensional combustion waves arising in the presence of a competitive endothermic reaction

2019 ◽  
Vol 60 ◽  
pp. C95-C108
Author(s):  
Simon Watt ◽  
Zhejun Huang ◽  
Harvinder Sidhu
Keyword(s):  
Period Doubling ◽  
Two Dimensions ◽  
Reaction Diffusion Equations ◽  
Endothermic Reaction ◽  
Combustion Waves ◽  
Complex Behaviour ◽  
Combustion Dynamics ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Appl Math

We consider a system of reaction-diffusion equations describing combustion dynamics. The reaction is assumed to undergo two competitive reactions, one which is exothermic and one which is endothermic. The one-dimensional model has been shown to exhibit complex behaviour, from propagating combustion waves with a constant speed to period doubling cascades and the possibility of chaotic wave speeds. In this study, we extend the combustion model from one to two dimensions by exploring a model of an insulated strip with no heat loss and axially symmetric spread. In particular, we compare and contrast the behaviour of the systems in one and two dimensions. References J. D. Buckmaster and G. S. S. Ludford. Theory of Laminar Flames. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, 1982. doi:10.1017/CBO9780511569531. V. Gubernov, A. Kolobov, A. Polezhaev, H. Sidhu, and G. Mercer. Period doubling and chaotic transient in a model of chain-branching combustion wave propagation. P. Roy. Soc. A Math. Phy., 466:27472769, 2010. doi:10.1098/rspa.2009.0668. A. Hmaidi, A. C. McIntosh, and J. Brindley. A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction. Combust. Theor. Model., 14:893920, 2010. doi:10.1080/13647830.2010.519050. G. N. Mercer and R. O. Weber. Combustion waves in two dimensions and their one-dimensional approximation. Combust. Theor. Model., 1:157165, 1997. doi:10.1088/1364-7830/1/2/002. J. J. Sharples, H. S. Sidhu, A. C. McIntosh, J. Brindley, and V. V. Gubernov. Analysis of combustion waves arising in the presence of a competitive endothermic reaction. IMA J. Appl. Math., 77:1831, 2012. doi:10.1093/imamat/hxr072. S. D. Watt, R. O. Weber, H. S. Sidhu, and G. N. Mercer. A weight-function approach for determining watershed initial conditions for combustion waves. IMA J. Appl. Math., 62:195206, 1999. doi:10.1093/imamat/62.2.195.

Perceived Mutual Understanding (PMU)

2019 ◽  
Vol 35 (1) ◽  
pp. 98-108 ◽  
Author(s):  
Michael J. Burtscher ◽  
Jeannette Oostlander
Keyword(s):  
Mutual Understanding ◽  
Team Cognition ◽  
Internal Reliability ◽  
Confirmatory Factor Analyses ◽  
Team Processes ◽  
One Dimensional ◽  
Item Parameters ◽  
Three Samples ◽  
Confirmatory Factor ◽  
The Individual

Abstract. Team cognition plays an important role in predicting team processes and outcomes. Thus far, research has focused on structured cognition while paying little attention to perceptual cognition. The lack of research on perceptual team cognition can be attributed to the absence of an appropriate measure. To address this gap, we introduce the construct of perceived mutual understanding (PMU) as a type of perceptual team cognition and describe the development of a respective measure – the PMU-scale. Based on three samples from different team settings ( NTotal = 566), our findings show that the scale has good psychometric properties – both at the individual as well as at the team-level. Item parameters were improved during a multistage process. Exploratory as well as confirmatory factor analyses indicate that PMU is a one-dimensional construct. The scale demonstrates sufficient internal reliability. Correlational analyses provide initial proof of construct validity. Finally, common indicators for inter-rater reliability and inter-rater agreement suggest that treating PMU as a team-level construct is justified. The PMU-scale represents a convenient and versatile measure that will potentially foster empirical research on perceptual team cognition and thereby contribute to the advancement of team cognition research in general.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann
Keyword(s):  
Magnetic Fields ◽  
Shock Waves ◽  
Physical Model ◽  
Spectroscopic Method ◽  
Experimental Results ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

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