COOPERATIVE PHASE DYNAMICS IN COUPLED NEPHRONS

2001 ◽  
Vol 15 (23) ◽  
pp. 3079-3098 ◽  
Author(s):  
D. E. POSTNOV ◽  
O. V. SOSNOVTSEVA ◽  
E. MOSEKILDE ◽  
N.-H. HOLSTEIN-RATHLOU
Keyword(s):  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Functional Unit ◽  
Flow Regulation ◽  
Tubuloglomerular Feedback ◽  
Phase Dynamics ◽  
The Individual ◽  
Fast Oscillations ◽  
Coherent Behavior ◽  
Different Time Scales

The individual functional unit of the kidney (the nephron) displays oscillations in its pressure and flow regulation at two different time scales: Relatively fast oscillations associated with the myogenic dynamics of the afferent arteriole, and slower oscillations related with a delay in the tubuloglomerular feedback. Neighboring nephrons interact via vascularly propagated signals. We study the appearance of various forms of coherent behavior in a model of two such interacting nephrons. Among the observed phenomena are in-phase and anti-phase synchronization of chaotic dynamics, multistability, and partial phase synchronization in which the nephrons attain a state of chaotic phase synchronization with respect to their slow dynamics, but the fast dynamics remains desynchronized.

scholarly journals Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

2019 ◽  
Vol 14 (2) ◽  
pp. 588-611
Author(s):  
M.P. Kulakov ◽  
E.V. Kurilova ◽  
E.Ya. Frisman
Keyword(s):  
Phase Synchronization ◽  
Oscillation Period ◽  
Logistic Growth ◽  
Predator Prey ◽  
Different Types ◽  
The Difference ◽  
Minimum Numbers ◽  
Fast Oscillations ◽  
Bursting Activity ◽  
Type Ii Functional Response

The papers is devoted to a model for two non-identical predator-prey communities coupled by migration and characterized by logistic growth of prey and Holling type II functional response. The coupling is a predator migration at constant weak rate. The non-identity is the difference in the prey growth rates or predator mortalities in each patch. We studied the equilibrium states of model and scenarios of loss of their stability and emerge of complex periodic solutions. It was shown that in some domains of the parameter space there is a bursting activity which are that the dynamics of two communities contain segments of slowly resting dynamic (as part of a fast-slow cycle or canard) and regular bursts of spikes. In the resting part, the dynamics of the second community, as a rule, follow the slow changes in the first community, i.e. the dynamics in different patches are synchronous. But in the fast part there is only phase synchronization between the fast-slow cycle in first patch and bursts in second. We classified the scenarios of transition between different types of bursting activity by location spiking manifold and canard. These types differ not so much in size, shape or numbers of spikes as in the order of bursts emerge relative a slow-fast cycle. In a typical case the start of burst (divergent fast oscillations) coincides with the minimum numbers or quasi-extinction of prey in the first patch. After a rapid increase in the prey number in the first patch, diverging fluctuations give way to damped in the second patch. Such dynamics correspond to the rhombus-wave shape of spikes cluster. Another case is interesting, when the burst of spikes is formed after the full recovery of prey and with a certain predator number in the first patch. In this case, the spikes cluster takes the shape of a triangle-wave or a truncated rhombus-wave. It was shown that transitions between these types of bursts are accompanied by a change in the oscillation period and the degree of synchronization. Triangular-wave bursters correspond to complete synchronization of the predator dynamics in the resting part and rhomboid-wave correspond to antiphase synchronization. In the fast part with many spikes, communities are completely asynchronous to each other.

PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (30) ◽  
pp. 5715-5726
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Coupled Oscillators ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics ◽  
Diffuse Clouds

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.

PHASE DYNAMICS OF COMPLEX-VALUED NEURAL NETWORKS AND ITS APPLICATION TO TRAFFIC SIGNAL CONTROL

2005 ◽  
Vol 15 (01n02) ◽  
pp. 111-120 ◽  
Author(s):  
IKUKO NISHIKAWA ◽  
TAKESHI IRITANI ◽  
KAZUTOSHI SAKAKIBARA ◽  
YASUAKI KUROE
Keyword(s):  
Phase Synchronization ◽  
Coupled System ◽  
Traffic Signals ◽  
Activation Function ◽  
Traffic Signal Control ◽  
Phase Oscillators ◽  
Hopfield Networks ◽  
Synchronization Mechanism ◽  
Phase Dynamics ◽  
Complex Valued

Complex-valued Hopfield networks which possess the energy function are analyzed. The dynamics of the network with certain forms of an activation function is decomposable into the dynamics of the amplitude and phase of each neuron. Then the phase dynamics is described as a coupled system of phase oscillators with a pair-wise sinusoidal interaction. Therefore its phase synchronization mechanism is useful for the area-wide offset control of the traffic signals. The computer simulations show the effectiveness under the various traffic conditions.

The step response: a method to characterize mechanisms of renal blood flow autoregulation

2003 ◽  
Vol 285 (4) ◽  
pp. F758-F764 ◽  
Author(s):  
T. Wronski ◽  
E. Seeliger ◽  
P. B. Persson ◽  
C. Forner ◽  
C. Fichtner ◽  
...  
Keyword(s):  
Blood Flow ◽  
Renal Blood Flow ◽  
Renal Perfusion ◽  
Oscillation Period ◽  
Tubuloglomerular Feedback ◽  
Step Response ◽  
Myogenic Response ◽  
Renal Vasculature ◽  
The Individual ◽  
Reported Data

Response of renal vasculature to changes in renal perfusion pressure (RPP) involves mechanisms with different frequency characteristics. Autoregulation of renal blood flow (RBF) is mediated by the rapid myogenic response, by the slower tubuloglomerular feedback (TGF) mechanism, and, possibly, by an even slower third mechanism. To evaluate the individual contribution of these mechanisms to RBF autoregulation, we analyzed the response of RBF to a step increase in RPP. In anesthetized rats, the suprarenal aorta was occluded for 30 s, and then the occlusion was released to induce a step increase in RPP. Three dampened oscillations were observed; their oscillation periods ranged from 9.5 to 13 s, from 34.2 to 38.6 s, and from 100.5 to 132.2 s, respectively. The two faster oscillations correspond with previously reported data on the myogenic mechanism and the TGF. In accordance, after furosemide, the amplitude of the intermediate oscillation was significantly reduced. Inhibition of nitric oxide synthesis by Nω-nitro-l-arginine methyl ester significantly increased the amplitude of the 10-s oscillation. It is concluded that the parameters of the dampened oscillations induced by the step increase in RPP reflect properties of autoregulatory mechanisms. The oscillation period characterizes the individual mechanism, the dampening is a measure for the stability of the regulation, and the square of the amplitudes characterizes the power of the respective mechanism. In addition to the myogenic response and the TGF, a third rather slow mechanism of RBF autoregulation exists.

Multinephron dynamics on the renal vascular network

2013 ◽  
Vol 304 (1) ◽  
pp. F88-F102 ◽  
Author(s):  
Donald J. Marsh ◽  
Anthony S. Wexler ◽  
Alexey Brazhe ◽  
Dmitri E. Postnov ◽  
Olga V. Sosnovtseva ◽  
...  
Keyword(s):  
Blood Flow ◽  
Smooth Muscle ◽  
Information Transfer ◽  
Phase Synchronization ◽  
Low Frequency ◽  
Vascular Network ◽  
Tubuloglomerular Feedback ◽  
Symmetric Model ◽  
Flow Measurements ◽  
Electrical Signals

Tubuloglomerular feedback (TGF) and the myogenic mechanism combine in each nephron to regulate blood flow and glomerular filtration rate. Both mechanisms are nonlinear, generate self-sustained oscillations, and interact as their signals converge on arteriolar smooth muscle, forming a regulatory ensemble. Ensembles may synchronize. Smooth muscle cells in the ensemble depolarize periodically, generating electrical signals that propagate along the vascular network. We developed a mathematical model of a nephron-vascular network, with 16 versions of a single nephron model containing representations of both mechanisms in the regulatory ensemble, to examine the effects of network structure on nephron synchronization. Symmetry, as a property of a network, facilitates synchronization. Nephrons received blood from a symmetric electrically conductive vascular tree. Symmetry was created by using identical nephron models at each of the 16 sites and symmetry breaking by varying nephron length. The symmetric model achieved synchronization of all elements in the network. As little as 1% variation in nephron length caused extensive desynchronization, although synchronization was maintained in small nephron clusters. In-phase synchronization predominated among nephrons separated by one or three vascular nodes and antiphase synchronization for five or seven nodes of separation. Nephron dynamics were irregular and contained low-frequency fluctuations. Results are consistent with simultaneous blood flow measurements in multiple nephrons. An interaction between electrical signals propagated through the network to cause synchronization; variation in vascular pressure at vessel bifurcations was a principal cause of desynchronization. The results suggest that the vasculature supplies blood to nephrons but also engages in robust information transfer.

Frequency encoding in renal blood flow regulation

2005 ◽  
Vol 288 (5) ◽  
pp. R1160-R1167 ◽  
Author(s):  
Donald J. Marsh ◽  
Olga V. Sosnovtseva ◽  
Alexey N. Pavlov ◽  
Kay-Pong Yip ◽  
Niels-Henrik Holstein-Rathlou
Keyword(s):  
Blood Pressure ◽  
Blood Flow ◽  
Renal Blood Flow ◽  
Amplitude Modulation ◽  
Wavelet Transforms ◽  
Modulation Frequency ◽  
Flow Regulation ◽  
Tubuloglomerular Feedback ◽  
Conscious Rat ◽  
Blood Flow Regulation

With a model of renal blood flow regulation, we examined consequences of tubuloglomerular feedback (TGF) coupling to the myogenic mechanism via voltage-gated Ca channels. The model reproduces the characteristic oscillations of the two mechanisms and predicts frequency and amplitude modulation of the myogenic oscillation by TGF. Analysis by wavelet transforms of single-nephron blood flow confirms that both amplitude and frequency of the myogenic oscillation are modulated by TGF. We developed a double-wavelet transform technique to estimate modulation frequency. Median value of the ratio of modulation frequency to TGF frequency in measurements from 10 rats was 0.95 for amplitude modulation and 0.97 for frequency modulation, a result consistent with TGF as the modulating signal. The simulation predicted that the modulation was regular, while the experimental data showed much greater variability from one TGF cycle to the next. We used a blood pressure signal recorded by telemetry from a conscious rat as the input to the model. Blood pressure fluctuations induced variability in the modulation records similar to those found in the nephron blood flow results. Frequency and amplitude modulation can provide robust communication between TGF and the myogenic mechanism.

STIMULUS-INDUCED CHAOTIC SYNCHRONIZATION OF CHUA'S OSCILLATORS

2006 ◽  
Vol 16 (10) ◽  
pp. 2843-2853
Author(s):  
V. V. KLINSHOV ◽  
V. B. KAZANTSEV ◽  
V. I. NEKORKIN
Keyword(s):  
Initial Phase ◽  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Cluster Formation ◽  
Time Moment ◽  
Chaotic Oscillation ◽  
Single Pulse ◽  
Chaotic Synchronization ◽  
Phase Reset ◽  
Chaotic Oscillators

The problem of phase synchronization of Chua's chaotic oscillators is investigated. We consider Chua's circuit when it exhibits a chaotic attractor and apply a single pulse stimulus. It is shown that under certain conditions the system displays self-referential phase reset (SPR) phenomenon. This is a case when the reset phase of the chaotic oscillation is independent on the initial phase, hence on the time moment when the stimulus has been applied. In an ensemble of chaotic oscillators simultaneously stimulated, the SPR yields mutual phase coherence or synchronization between the units. We describe basic dynamical mechanisms of the effect and show how it can be used for controllable cluster formation and for the control of chaotic dynamics.

POPULATION GROWTH MODELING WITH BOOM AND BUST PATTERNS: THE IMPULSIVE DIFFERENTIAL EQUATION FORMALISM

2015 ◽  
Vol 23 (supp01) ◽  
pp. S135-S149 ◽  
Author(s):  
FERNANDO CÓRDOVA-LEPE ◽  
GONZALO ROBLEDO ◽  
JAVIER CABRERA-VILLEGAS
Keyword(s):  
Differential Equation ◽  
Population Dynamics ◽  
Time Scales ◽  
Chaotic Dynamics ◽  
Impulsive Differential Equation ◽  
Dynamical Behavior ◽  
Single Species ◽  
Open Problems ◽  
Boom And Bust ◽  
Different Time Scales

This note gives an overview on basic mathematical models describing the population dynamics of a single species whose vital dynamics has different time scales. We present five cases combining two time–scales with Malthusian growth in at least one scale. The dynamical behavior shows a progressive complexity, from "naive" to chaotic dynamics (in the Li–Yorke's sense). In addition, some open problems and new results are presented.

TRACKING PHASE SYNCHRONIZATION OF TWO COUPLED RÖSSLER OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (23) ◽  
pp. 4809-4816 ◽  
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupling Parameter ◽  
Primary Resonance ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength.

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