Search results for "Chaotic"
showing 10 items of 297 documents
Seasonal genetic variation associated with population dynamics of a poecilogonous polychaete worm
2017
Poecilogonous species show variation in developmental mode, with larvae that differ both morphologically and ecologically. The spionid polychaete Pygospio elegans shows variation in developmental mode not only between populations, but also seasonally within populations. We investigated the consequences of this developmental polymorphism on the spatial and seasonal genetic structure of P. elegans at four sites in the Danish Isefjord‐Roskilde‐Fjord estuary at six time points, from March 2014 until February 2015. We found genetic differentiation between our sampling sites as well as seasonal differentiation at two of the sites. The seasonal genetic shift correlated with the appearance of new s…
Dynamic complexities in host-parasitoid interaction
1999
In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, the investigations of complex population dynamics have mainly concentrated on single populations and not on higher dimensional ecological systems. Here we report a detailed study of the complicated dynamics occurring in a basic discrete-time model of host-parasitoid interaction. The complexities include (a) non-unique dynamics, meaning that several attractors coexist, (b) basins of attraction (defined as the set of the initial conditions leading to a certain type of an attractor) with fractal properties (pattern of…
Non-unique population dynamics: basic patterns
2000
We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing host‐macroparasite and host‐parasitoid interspecific interactions. In general, several types of attractors, e.g. point equilibria vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attrac…
Convergence of direct recursive algorithm for identification of Preisach hysteresis model with stochastic input
2015
We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive sc…
New Approach of Controlling Cardiac Alternans
2018
The alternans of the cardiac action potential duration is a pathological rhythm. It is considered to be relating to the onset of ventricular fibrillation and sudden cardiac death. It is well known that, the predictive control is among the control methods that use the chaos to stabilize the unstable fixed point. Firstly, we show that alternans (or period-2 orbit) can be suppressed temporally by the predictive control of the periodic state of the system. Secondly, we determine an estimation of the size of a restricted attraction's basin of the unstable equilibrium point representing the unstable regular rhythm stabilized by the control. This result allows the application of predictive control…
Families of piecewise linear maps with constant Lyapunov exponent
2012
We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.
A note on higher order Melnikov functions
2005
We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.
Strange Attractors, Chaotic Behavior and Informational Aspects of Sleep EEG Data
1992
In order to perform a nonlinear dimensional analysis of the sleep EEG, we applied an algorithm proposed to calculate the correlation dimension D2 of different sleep stages. D2 characterizes the dynamics of the sleep EEG, estimates the degrees of freedom, and describes the complexity of the signal under study. An attempt is made to correlate dimensionality analysis and informational aspects of the sleep EEG. Information processing by the brain during different sleep stages of healthy subjects under the influence of lorazepam and in unmedicated acute schizophrenics is estimated.
Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep
1993
Under selected conditions, nonlinear dynamical systems, which can be described by deterministic models, are able to generate so-called deterministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separated for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a deterministic process which should not be mistaken for simple noise. The calcu…
The calculation of the first positive Lyapunov exponent in sleep EEG data
1993
To help determine if the EEG is quasiperiodic or chaotic we performed a new analysis by calculating the first positive Lyapunov exponent L1 from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L1 is zero for periodic as well as quasiperiodic processes, but positive in case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L1 for sleep EEG segments of 15 healthy male subjects corresponding to sleep stages I, II, III, IV and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor simple noise. Moreover…