			Home About us Contact

Chaotic Behaviour (chaotic + behaviour)

Distribution by Scientific Domains

Engineering	42%

Selected Abstracts

Is a chaotic multi-fractal approach for rainfall possible?

HYDROLOGICAL PROCESSES, Issue 6 2001
Bellie Sivakumar
Abstract An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381,2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono-fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi-fractal approaches. The assumption behind multi-fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi-fractals. However, it has been observed recently that multi-fractal approaches might provide positive evidence of a multi-fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi-fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi-fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi-fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi-fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Hyperchaotic behaviour of two bi-directionally coupled Chua's circuits

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 6 2002
Barbara Cannas
Abstract In this paper, a non-linear bi-directional coupling of two Chua's circuits is presented. The coupling is obtained by using polynomial functions that are symmetric with respect to the state variables of the two Chua's circuits. Both a transverse and a tangent system are studied to ensure a global validity of the results in the state space. First, it is shown that the transverse system is an autonomous Chua's circuit, which directly allows the evaluation of the conditions on its chaotic behaviour, i.e. the absence of synchronization between the coupled circuits. Moreover, it is demonstrated that the tangent system is also a Chua's circuit, forced by the transverse system; therefore, its dynamics is ruled by a time-dependent equation. Thus, the calculus of conditional Lyapunov exponents is necessary in order to exclude antisynchronization along the tangent manifold. The properties of the transverse and tangent systems simplify the study of the coupled Chua's circuits and the determination of the conditions on their hyperchaotic behaviour. In particular, it is shown that hyperchaotic behaviour occurs for proper values of the coupling strength between the two Chua's circuits. Finally, numerical examples are given and discussed. Copyright © 2002 John Wiley & Sons, Ltd. [source]

On the invariant measure for the quasi-linear Lasota equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007
Antoni Leon Dawidowicz
Abstract The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiello,skiego, Pr. Mat. 1982; 23:117,123; Ann. Pol. Math. 1983; XLI:129,137; J. Differential Equations 2004; 196:448,465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi-linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiello,skiego, Pr. Mat. 1982; 23:117,123). Copyright © 2006 John Wiley & Sons, Ltd. [source]

Non-standard finite difference schemes for multi-dimensional second-order systems in non-smooth mechanics

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007
Yves Dumont
Abstract This work is an extension of the paper (Proc. R. Soc. London 2005; 461A:1927,1950) to impact oscillators with more than one degree of freedom. Given the complex and even chaotic behaviour of these non-smooth mechanical systems, it is essential to incorporate their qualitative physical properties, such as the impact law and the frequencies of the systems, into the envisaged numerical methods if the latter is to be reliable. Based on this strategy, we design several non-standard finite difference schemes. Apart from their excellent error bounds and unconditional stability, the schemes are analysed for their efficiency to preserve some important physical properties of the systems including, among others, the conservation of energy between consecutive impact times, the periodicity of the motion and the boundedness of the solutions. Numerical simulations that support the theory are provided. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Data assimilation with regularized nonlinear instabilities

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 648 2010
Henry D. I. Abarbanel
Abstract In variational formulations of data assimilation, the estimation of parameters or initial state values by a search for a minimum of a cost function can be hindered by the numerous local minima in the dependence of the cost function on those quantities. We argue that this is a result of instability on the synchronization manifold where the observations are required to match the model outputs in the situation where the data and the model are chaotic. The solution to this impediment to estimation is given as controls moving the positive conditional Lyapunov exponents on the synchronization manifold to negative values and adding to the cost function a penalty that drives those controls to zero as a result of the optimization process implementing the assimilation. This is seen as the solution to the proper size of ,nudging' terms: they are zero once the estimation has been completed, leaving only the physics of the problem to govern forecasts after the assimilation window. We show how this procedure, called Dynamical State and Parameter Estimation (DSPE), works in the case of the Lorenz96 model with nine dynamical variables. Using DSPE, we are able to accurately estimate the fixed parameter of this model and all of the state variables, observed and unobserved, over an assimilation time interval [0, T]. Using the state variables at T and the estimated fixed parameter, we are able to accurately forecast the state of the model for t > T to those times where the chaotic behaviour of the system interferes with forecast accuracy. Copyright © 2010 Royal Meteorological Society [source]

Is a chaotic multi-fractal approach for rainfall possible?

Awareness of early warning signs and help-seeking behaviours among patients with schizophrenia who utilize social rehabilitation facilities in Japan

JOURNAL OF PSYCHIATRIC & MENTAL HEALTH NURSING, Issue 8 2009
R. KOICHI rn phn ms
Accessible summary ,,Schizophrenia is characterized by the occurrence of psychotic relapses. When this happens, early warning signs such as delusions, hallucinations, thought incoherencies and serious chaotic behaviours occur. ,,In this study, 56.5% of participants who had a history at least one early help-seeking behaviour when they deteriorated was recognized from the following signs: sleep disorders, depression, hallucinations, nervousness, anxiety, fatigue, delusions, illusions and suicidal ideation. ,,Early help-seeking behaviours were related to the following factors: recognition of early warning signs during deterioration, consultation with non-professional and professional support persons during deterioration; consulting with public mental health workers; and living with family. Abstract The purpose of this study was to examine the relationship between early warning signs (EWS) and early help-seeking behaviours (HSB) and to identify the characteristics of patients with schizophrenia who sought early help. A cross-sectional study was carried out in 2004 using a self-reported questionnaire. Participants were recruited from social rehabilitation facilities for the mentally ill; 224 subjects participated, 170 of whom had schizophrenia. The survey included questions about demographic characteristics, self-care behaviours (HSB, recognition of EWS and others) and current service utilization and satisfaction. Fisher's exact test and Student's t -test were used to compare the characteristics of study participants. Logistic regression analyses were used to examine the association between recognition of EWS and early HSB. We found that 96 (56.5%) of 170 patients with schizophrenia reported at least one occasion of early HSB during their deterioration. Early HSB were related to the following factors: recognition of EWS, consultation with non-professional and professional support persons during deterioration, consulting with public mental health workers and living with family. Care and support should be offered to patients with schizophrenia to enable them to recognize their own mental deterioration. [source]