Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Nonlinear Dynamics”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7Linked to original sources
PubMed1997

Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings.

PURPOSE: An understanding of the principles governing the behavior of complex neuronal networks, in particular their capability of generating epileptic seizures implies the characterization of the conditions under which a transition from the interictal to the ictal state takes place. Signal analysis methods derived from the theory of nonlinear dynamics provide new tools to characterize the behavior of such networks, and are particularly relevant for the analysis of epileptiform activity. METHODS: We calculated the correlation dimension, tested for irreversibility, and made recurrence plots of EEG signals recorded intracranially both during interictal and ictal states in temporal lobe epilepsy patients who were surgical candidates. RESULTS: Epileptic seizure activity often, but not always, emerges as a low-dimensional oscillation. In general, the seizure behaves as a nonstationary phenomenon during which both phases of low and high complexity may occur. Nevertheless a low dimension may be found mainly in the zone of ictal onset and nearby structures. Both the zone of ictal onset and the pattern of propagation of seizure activity in the brain could be identified using this type of analysis. Furthermore, the results obtained were in close agreement with visual inspection of the EEG records. CONCLUSIONS: Application of these mathematical tools provides novel insights into the spatio-temporal dynamics of "epileptic brain states". In this way it may be of practical use in the localization of an epileptogenic region in the brain, and thus be of assistance in the presurgical evaluation of patients with localization-related epilepsy.

Adult↗
PubMed2004

Relation of depression to heart rate nonlinear dynamics in patients > or =60 years of age with recent unstable angina pectoris or acute myocardial infarction.

Depression is common among older patients and it has been related to a worsened coronary prognosis. The basis for this association is controversial. The aim of this study was to ascertain whether patients with a recent acute coronary event show depression-related changes of heart rate variability (HRV) nonlinear dynamics. Alterations of the HRV have been recently shown to predict mortality in patients recovering from an acute myocardial infarction. In 52 patients > or =60 years (52% women) with recent (within 24 to 72 hours) unstable angina pectoris or myocardial infarction, we obtained conventional time- and frequency-domain HRV measurements, along with nonlinear HRV measurements, including SD of the instantaneous beat-to-beat variability (SD1), scaling exponent alpha1 (alpha1), and approximate entropy (ApEn) from 10-minute RR-interval recordings. We also evaluated the presence of clinical depression and measured its severity by means of a 21-item Hamilton Depression Scale. On admission to the coronary care unit, 19 patients (37%) were depressed; alpha1 was higher (1.23 +/- 0.21 vs 1.03 +/- 0.30, p <0.05), whereas SD1 (10.4 +/- 3.7 vs 14.4 +/- 7.3, p <0.05) and ApEn (0.98 +/- 0.22 vs 1.16 +/- 0.15, p <0.001) were lower in depressed patients. Also, alpha1 increased (r = 0.31, p <0.05) and both SD1 (r = -0.46, p <0.01) and ApEn (r = -0.28, p <0.05) decreased with worsening depressive symptoms. In our sample, depression was associated with increased correlation and decreased complexity of the interbeat interval time series in older adults who had recently developed an acute coronary syndrome.

Aged↗
PubMed2002

Developmental trajectories, transitions, and nonlinear dynamical systems: a model of crime deceleration and desistance.

Research on crime-related developmental trajectories is reviewed with outcomes revealing the existence of several trajectories rather than a single general pattern. Each trajectory is marked by transitions that define the pattern's path and direction over time. These anticipated transitions differ from the unanticipated transitions known to precipitate crime deceleration and desistance. Borrowing principles from nonlinear dynamical systems theory--sensitive dependence on initial conditions, chaotic attractors, and self-organization in particular--this article offers a model of crime deceleration and desistance in which belief systems congruent with crime are altered in phases--initiation, transition, maintenance--to create belief systems incongruent with crime. The practical implications of this model are discussed and suggestions for future research are outlined.

Adolescent↗
PubMed1999

Nonlinear dynamics of giant resonances in atomic nuclei.

The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicates regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.

Journal Article↗
PubMed2005

A population-based model of the nonlinear dynamics of the thalamocortical feedback network displays intrinsic oscillations in the spindling (7-14 Hz) range.

The thalamocortical network is modelled using the Wilson-Cowan equations for neuronal population activity. We show that this population model with biologically derived parameters possesses intrinsic nonlinear oscillatory dynamics, and that the frequency of oscillation lies within the spindle range. Spindle oscillations are an early sleep oscillation characterized by high-frequency bursts of action potentials followed by a period of quiescence, at a frequency of 7-14 Hz. Spindles are generally regarded as being generated by intrathalamic circuitry, as decorticated thalamic slices and the isolated thalamic reticular nucleus exhibit spindles. However, the role of cortical feedback has been shown to regulate and synchronize the oscillation. Previous modelling studies have mainly used conductance-based models and hence the mechanism relied upon the inclusion of ionic currents, particularly the T-type calcium current. Here we demonstrate that spindle-frequency oscillatory activity can also arise from the nonlinear dynamics of the thalamocortical circuit, and we use bifurcation analysis to examine the robustness of this oscillation in terms of the functional range of the parameters used in the model. The results suggest that the thalamocortical circuit has intrinsic nonlinear population dynamics which are capable of providing robust support for oscillatory activity within the frequency range of spindle oscillations.

Animals↗
PubMed2004

Temporal order of nonlinear dynamics in human brain.

In previous spectral analysis investigations, we demonstrated that the spontaneous activity of the alpha EEG is not stationary but rather shows cyclic alterations with a circa 1-min periodicity. Following the conclusion that a power increase in the alpha band implies a neuronal synchronization, and vice versa, an associated decrease of the EEG complexity was postulated. Accordingly, a rhythmic variation, i.e., a temporal order of the nonlinear dynamics with similar period length, was expected. Bipolar 4-min EEG recordings were obtained from 20 awake subjects (mean age: 23.5+/-2.5 years) with eyes closed for the EEG leads C3, C4, Oz, and Fz according to the 10-20 system. For the automatic evaluation of spontaneous alterations of complexity, a sliding computation of the so-called correlation dimension, using an analysis window length of 20 s continuously shifted by 1 s, was performed. The time series of complexity exhibited an oscillatory behavior with a mean period length of 58.7 s; the Friedman test statistic revealed no significant topological differences. For the rejection of the null hypothesis that the observed periodicity is a random one, two-group t-tests and ANOVA with repeated measures were performed, comparing the corresponding amplitudes and period lengths with those derived from 20 pseudo-random signals (taken from a multivariate Gaussian normal distribution). The mean relative change of EEG complexity was highly significantly increased (P<0.0001) compared to that of random data. Likewise, the difference of mean period lengths was also significant (P<0.01). The results indicate that the coupling strength of the neural network of the brain changes periodically, with a cyclic alteration from a central to a parallel processing mode of information, reflecting state transitions from synchronized, low-complex EEG activity to desynchronized high-complex activity, and vice versa. Various neuronal control mechanisms that may be acting as pacemakers responsible for the temporal order of such transients are discussed. A disturbance of the temporal order may be of pathophysiological significance.

Action Potentials↗
PubMed2003

Nonlinear dynamics in laser polarization conversion by stimulated scattering in nematic liquid crystal films.

We present a study of the nonlinear dynamics of a coherent polarization conversion process in nematic liquid crystal films. This effect is mediated by two-beam coupling between the incident polarized laser and its orthogonally polarized (lower-frequency) noise component scattered by the director axis fluctuations. A complete model for the director dynamics derived from the basic equations is presented. The existence of complex, time-, and intensity-dependent dynamics of the director motion such as oscillations and various bifurcations including period doubling is revealed.

Journal Article↗
PubMed2004

Reconstruction of shared nonlinear dynamics in a network.

We study a general physical network consisting of a collection of response systems with complex nonlinear dynamics, influenced by a common driver. The goal is to reconstruct dynamics, regular or chaotic, that are common to all of the response systems, working from simultaneous time series measured at the responses systems only. A fundamental theorem is stated concerning the reconstruction of the common driver. An algorithm is developed, based on the theorem, to carry out the reconstruction, and is demonstrated with several examples.

Journal Article↗
PubMed2007

Do nonlinear dynamics in economics amount to a Kuhnian paradigm shift?

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies "free enterprise" with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it.

Journal Article↗
PubMed2001

Repetitive apneas reduce nonlinear dynamical complexity of the human cardiovascular control system.

We tested the hypothesis that intermittent apneas performed by awake subjects simulate obstructive sleep apnea (OSA) and change dynamic complexity of the cardiovascular control system by repetitive short time stimulation of arterial chemoreceptors. Correlation dimension (CD) and reccurent plot quantification calculated as ratio % determinism versus % recurrence (RDR) were used.as indices of chaotic dynamics. Thirty three normotensive subjects of mean age 21,58 +/- 4,1 performed 10 voluntary apneas 1 min. each separated by 1 min free breathing period. Systolic (SYS), diastolic (DIAS) arterial blood pressure was continuously recorded by finger volume clamp. Stroke volume (SV) was estimated by pulse pressure analysis. Cardiac output (CO) and total peripheral resistance (TPR) were calculated by Portapress system. Cardiac inter-beat interval (IBI) was measured from R-R intervals of ECG. Standard deviation (SD), an index of linear variability, was calculated in 1 min epoch. Dynamics of cardiovascular variables was computed in each subject during 20 min. rest (C), 20 min. of 10 apneas, 1 min each, separated by 1 min free breathing (A), and in 20 min. recovery free breathing (R). In A period CD of all circulatory variables was significantly reduced and RDR augmented. In 23 out of 33 subjects decreased nonlinear dynamics of TPR was carried over from A to R. In contrast, SD increased significantly in A. In conclusion, intermittent brief chemoreflex stimulations by repetitive apneas increase blood pressure and TPR and decrease chaotic behaviour and complexity of the cardiovascular autonomic control system, presumably by inhibition of some regulatory loops such as baroreflex, less vital for survival at oxygen deprivation. Reduced complexity could be implicated in the mechanism of arterial hypertension linked with OSA.

Adolescent↗
PubMed1998

Arterial vasomotion: effect of flow and evidence of nonlinear dynamics.

Vasomotion has been studied on segments of rat mesenteric and femoral arteries perfused in vitro. We have investigated 1) the effect of perfusion flow on the characteristics of vasomotion and 2) the nature and patterns of vasomotion. We have found that perfusion flow is not a control parameter that contributes to the genesis of vasomotion but that it affects, in most cases only slightly, the frequency and amplitude of vasomotion. We have found evidence that vasomotion is low-dimensional chaotic. The correlation dimension ranged between 2 and 4, and the average Lyapunov's coefficient was approximately 0.1. A great variety of vasomotion patterns was observed with features that are typical of nonlinear deterministic systems: regular and irregular vasomotion, quasiperiodicity, period doubling and higher-order periods, intermittency, mixed modes, and bursting activity. Vasomotion patterns appeared occasionally to be highly sensitive to perturbations in perfusion flow, which also supported the existence of nonlinear dynamics. Finally, entrainment (phase locking) was observed when arteries were perfused with oscillatory flow with frequency in the neighborhood of the frequency of vasomotion.

Animals↗
PubMedDate not supplied

Adaptive regulation of the nonlinear dynamics of electrical activity of the brain.

A programmable system was used to provide contingent reinforcement of EEG cycles corresponding to a selected criterion in a dynamic regime. Use of automated reinforcing stimulation of emotionally positive zones of the hypothalamus led to a significant increase in the number of cycles with the characteristics specified by the dynamic regime within the dominant EEG frequency bands. This effect lasted for some time after withdrawal of reinforcing stimulation, and then died down gradually. These changes in the EEG activity structure did not occur in conditions of nonassociated hypothalamic stimulation. Pseudoreinforced background EEG cycles showed complex nonlinear dynamics with competitive interactions between processes in which the large dimensionality of the attractor was difficult to interpret because of indeterminacy in the trends of the dominant process. In contingent hypothalamic stimulation, the form of the correlation integral changed towards a predominance of a single nonlinear process determining all the activity recorded. In fact, a single dominant nonlinear process was formed, which became responsible for the entire dynamics of the system with concordance of its internal structure.

Adaptation, Physiological↗
PubMed2004

Nonlinear dynamics of semiconductor lasers with active optical feedback.

An in-depth theoretical as well as experimental analysis of the nonlinear dynamics in semiconductor lasers with active optical feedback is presented. Use of a monolithically integrated multisection device of submillimeter total length provides access to the short-cavity regime. By introducing an amplifier section as a special feature, phase and strength of the feedback can be separately tuned. In this way, the number of modes involved in the laser action can be adjusted. We predict and observe specific dynamical scenarios. Bifurcations mediate various transitions in the device output, from single-mode steadystate to self-pulsation and between different kinds of self-pulsations, reaching eventually chaotic behavior in the multimode limit.

Journal Article↗
PubMed2006

Generalized models as a universal approach to the analysis of nonlinear dynamical systems.

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socioeconomic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web.

Journal Article↗
PubMed2001

Complex nonlinear dynamics of the Hodgkin-Huxley equations induced by time scale changes.

The Hodgkin-Huxley equations with a slight modification are investigated, in which the inactivation process (h) of sodium channels or the activation process of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau potential, such as in heart muscle cells, to chaotic bursting firings. When h is slowed down--differently from the case of n variable being slow --chaotic bursting oscillations are observed for a wide range of parameter values although both variables cause a decrease in the membrane potential. The underlying nonlinear dynamics of various action potentials are analyzed using bifurcation theory and a so-called slow-fast decomposition analysis. It is shown that a simple topological property of the equilibrium curves of slow and fast subsystems is essential to the production of chaotic oscillations, and this is the cause of the large difference in global firing characteristics between the h-slow and n-slow cases.

Action Potentials↗
PubMedDate not supplied

Adaptive terminal sliding mode control for high-order nonlinear dynamic systems.

An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.

Journal Article↗
PubMed1992

Stripe selection: an intrinsic property of some pattern-forming models with nonlinear dynamics.

In two-dimensional pattern formation, the genesis of stripped rather than spotted patterns may involve preexisting spatial asymmetries, such as unidirectional gradients or asymmetric shape of the pattern-forming domain. In the absence of such asymmetries, some kinds of nonlinear dynamics still lead to striped rather than spotted patterns. We have studied the latter effect both by extensive computer experiments on a range of nonlinear models and by mathematical analysis. We conclude that, when the dynamic equations are written in terms of departure from the unpatterned state, the presence of nonlinearities which are odd functions of these departures (e.g., cubic terms) together with absence of even nonlinearities (e.g., quadratic terms) ensures stripe formation. In computer experiments, we have studied the dynamics of two-morphogen reaction-diffusion models. The mathematical analysis presented in the Appendix shows that the same property exists in more generalized models for pattern formation in the primary visual cortex.

Animals↗
PubMed2002

Nonlinear dynamics of a Bragg cell under intensity feedback in the near-Bragg, four-order regime.

A detailed examination of the nonlinear dynamical behavior of an acousto-optic Bragg cell in the near-Bragg regime of operation for the case of four scattered orders under intensity feedback is carried out. This problem is an extension of the standard ideal-Bragg feedback model whereby traditionally bistability, hysteresis, and chaotic oscillations are observed under zeroth- or first-order feedback of the scattered light. For the present case, the closed-loop equations are developed from a priori knowledge of the open-loop analytical solutions for four-order near-Bragg scattering. The results, obtained via computer simulation, reveal a variety of interesting dynamics, including bistability, bifurcation, hysteresis, chaotic oscillations (including in this case the relatively uncommon period-three behavior, in addition to the more usual period-doubling phenomenon en route to chaos), and potentially useful parametric dependence of these features. The observed results are interpreted in terms of system behavior for varying feedback gain and bias, the so-called Klein-Cook parameter Q, and time delay, and are compared with earlier work based on the ideal Bragg regime.

Journal Article↗