3,465 research outputs found
Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling
Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region.
We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell–cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region.
However, real tissues are heterogeneous with spatial changes in cell–cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell–cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient
Synthesizing attractors of Hindmarsh-Rose neuronal systems
In this paper a periodic parameter switching scheme is applied to the
Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show
numerically, via computer graphic simulations, that the obtained synthesized
attractor belongs to the class of all admissible attractors for the
Hindmarsh-Rose neuronal system and matches the averaged attractor obtained with
the control parameter replaced with the averaged switched parameter values.
This feature allows us to imagine that living beings are able to maintain vital
behavior while the control parameter switches so that their dynamical behavior
is suitable for the given environment.Comment: published in Nonlinear Dynamic
Universality in Systems with Power-Law Memory and Fractional Dynamics
There are a few different ways to extend regular nonlinear dynamical systems
by introducing power-law memory or considering fractional
differential/difference equations instead of integer ones. This extension
allows the introduction of families of nonlinear dynamical systems converging
to regular systems in the case of an integer power-law memory or an integer
order of derivatives/differences. The examples considered in this review
include the logistic family of maps (converging in the case of the first order
difference to the regular logistic map), the universal family of maps, and the
standard family of maps (the latter two converging, in the case of the second
difference, to the regular universal and standard maps). Correspondingly, the
phenomenon of transition to chaos through a period doubling cascade of
bifurcations in regular nonlinear systems, known as "universality", can be
extended to fractional maps, which are maps with power-/asymptotically
power-law memory. The new features of universality, including cascades of
bifurcations on single trajectories, which appear in fractional (with memory)
nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201
Using Delay-Differential Equations for Modeling Calcium Cycling in Cardiac Myocytes
The cycling of calcium at the intracellular level of cardiac cells plays a key role in the excitation-contraction process. The interplay between ionic currents, buffering agents, and calcium release from the sarcoplasmic reticulum (SR) is a complex system that has been shown experimentally to exhibit complex dynamics including period-2 states (alternans) and higher-order rhythms. Many of the calcium cycling activities involve the sensing, binding, or diffusion of calcium between intracellular compartments; these are physical processes that take time and typically are modeled by “relaxation” equations where the steady-state value and time course of a particular variable are specified through an ordinary differential equation (ODE) with a time constant. An alternative approach is to use delay-differential equations (DDEs), where the delays in the system correspond to non-instantaneous events. In this thesis, we present a thorough overview of results from calcium cycling experiments and proposed intracellular calcium cycling models, as well as the context of alternans and delay-differential equations in cardiac modeling. We utilize a DDE to model the diffusion of calcium through the SR by replacing the relaxation ODE typically used for this process. The relaxation time constant τa is replaced by a delay δj, which could also be interpreted as the refractoriness of ryanodine receptor channels after releasing calcium from the sarcoplasmic reticulum. This is the first application of delay-differential equations to modeling calcium cycling dynamics, and to modeling cardiac systems at the cellular level. We analyzed the dynamical behaviors of the system and focus on the factors that have been shown to produce alternans and irregular dynamics in experiments and models with cardiac myocytes. We found that chaotic calcium dynamics could occur even for a more physiologically revelant SR calcium release slope than comparable ODE models. Increasing the SR release slope did not affect the calcium dynamics, but only shifted behavior down to lower values of the delay, allowing alternans, higher-order behavior, and chaos to occur for smaller delays than in simulations with a normal SR release slope. For moderate values of the delay, solely alternans and 1:1 steady-state behavior were observed. Above a particular threshold value for the delay, chaos appeared in the dynamics and further increasing the delay caused the system to destabilize under broader ranges of periods. We also compare our results with other models of intracellular calcium cycling and suggest promising avenues for further development of our preliminary work
Hysteresis in Adiabatic Dynamical Systems: an Introduction
We give a nontechnical description of the behaviour of dynamical systems
governed by two distinct time scales. We discuss in particular memory effects,
such as bifurcation delay and hysteresis, and comment the scaling behaviour of
hysteresis cycles. These properties are illustrated on a few simple examples.Comment: 28 pages, 10 ps figures, AMS-LaTeX. This is the introduction of my
Ph.D. dissertation, available at
http://dpwww.epfl.ch/instituts/ipt/berglund/these.htm
Recent Advances and Applications of Fractional-Order Neural Networks
This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed
- …