THE DYNAMICS OF TWO PULSE-COUPLED RELAXATION OSCILLATORS

1992 ◽  
Vol 02 (02) ◽  
pp. 341-352 ◽  
Author(s):  
ADAM A. BRAILOVE
Keyword(s):  
Natural Frequencies ◽  
Initial Conditions ◽  
Periodic Trajectory ◽  
Realistic Case ◽  
Relaxation Oscillators ◽  
Integrate And Fire ◽  
Necessary And Sufficient ◽  
Parameter Values

The dynamics of a pair of coupled integrate-and-fire oscillators is studied. Previous work by Mirollo and Strogatz is extended here to include the more realistic case in which the oscillators have different natural frequencies. It is shown that, given sufficient coupling, oscillators with arbitrary natural frequencies can always be made to synchronize. Furthermore, the condition necessary and sufficient for synchronization is determined. It is also shown that for any given set of parameter values there is a single periodic trajectory toward which all initial conditions are attracted: neither chaos nor quasiperiodicity is possible.

Synchronization in Relaxation Oscillator Networks with Conduction Delays

2001 ◽  
Vol 13 (5) ◽  
pp. 1003-1021 ◽  
Author(s):  
Jeffrey J. Fox ◽  
Ciriyam Jayaprakash ◽  
DeLiang Wang ◽  
Shannon R. Campbell
Keyword(s):  
Numerical Simulations ◽  
Coupled Oscillators ◽  
Initial Conditions ◽  
Relaxation Oscillator ◽  
Phase Lag ◽  
Relaxation Oscillators ◽  
Oscillator Networks ◽  
Coupled Networks ◽  
Parameter Values ◽  
Zero Phase

We study locally coupled networks of relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving zero phase-lag synchrony. Our mechanism is based on the observation that different rates of motion along different nullclines of the system can lead to synchrony in the presence of conduction delays. We analyze the system of two coupled oscillators and derive phase compression rates. This analysis indicates how to choose nullclines for individual relaxation oscillators in order to induce rapid synchrony. The numerical simulations demonstrate that our analytical results extend to locally coupled networks with conduction delays and that these networks can attain rapid synchrony with appropriately chosen nullclines and initial conditions. The robustness of the proposed mechanism is verified with respect to different nullclines, variations in parameter values, and initial conditions.

scholarly journals Predicting Experimental Sepsis Survival with a Mathematical Model of Acute Inflammation

2021 ◽  
Vol 1 ◽  
Author(s):  
Jared Barber ◽  
Amy Carpenter ◽  
Allison Torsey ◽  
Tyler Borgard ◽  
Rami A. Namas ◽  
...  
Keyword(s):  
Immune Response ◽  
Growth Rate ◽  
Inflammatory Response ◽  
Inflammatory Responses ◽  
Initial Conditions ◽  
Mortality Data ◽  
Experimental Sepsis ◽  
Initial Inoculum ◽  
Molecular Pattern ◽  
Parameter Values

Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels.

Condition Monitoring Technology for Connecting Part and Sliding Part of Reciprocating Compressor

2017 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Error Function ◽  
Connecting Rod ◽  
Value Analysis ◽  
Before And After ◽  
The Difference ◽  
Bending Modes ◽  
Parameter Values ◽  
The Mathematical Model

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.

Torsional damping of a back-to-back gearbox rig: Experimental measurements and frequency domain modelling

2002 ◽  
Vol 216 (2) ◽  
pp. 157-168 ◽  
Author(s):  
S J Drew ◽  
B J Stone
Keyword(s):  
Frequency Domain ◽  
Natural Frequencies ◽  
Model Parameters ◽  
Modal Damping ◽  
Torsional Damping ◽  
Analysis Of Results ◽  
Torsional Frequency ◽  
Signal Processing Methods ◽  
Parameter Values ◽  
Future Work

This paper is concerned with the experimental measurement and modelling of the torsional damping levels of a back-to-back gearbox rig. The aims of the investigation were to experimentally measure and analyse modal damping levels for the first nine torsional natural frequencies; to optimize damping parameters for modelling and to assess any limitations of the models for future work. Standard signal processing methods were used to determine modal damping levels from measured torsional frequency responses, with good confidence in the results. A damping sensitivity analysis for the two frequency domain receptance (FDR) models was used to determine optimum damping parameter values. Damping levels for six of nine natural frequencies were well matched with the experimental data. Discrepancies at other frequencies were attributed mainly to torsional-transverse coupling, present in the rig but not the model. Analysis of results for the ninth natural frequency determined a very low level of damping for the gearbox. It was also concluded that the model parameters may be used with confidence in a time domain receptance model for future investigations related to the test gearbox damping.

scholarly journals Existence of a Period-Two Solution in Linearizable Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
E. J. Janowski ◽  
M. R. S. Kulenović
Keyword(s):  
Difference Equation ◽  
Linear Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Minimal Period ◽  
Real Numbers ◽  
Existence And Nonexistence ◽  
The Difference ◽  
Necessary And Sufficient

Consider the difference equationxn+1=f(xn,…,xn−k),n=0,1,…,wherek∈{1,2,…}and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equationxn+l=∑i=1−lkgixn−i,n=0,1,…,wherel,k∈{1,2,…}and the functionsgi:ℝk+l→ℝ. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution whenl=1.

scholarly journals Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

2018 ◽  
Vol 23 (4) ◽  
pp. 65 ◽  
Author(s):  
Kaijun Peng ◽  
Jieqing Tan ◽  
Zhiming Li ◽  
Li Zhang
Keyword(s):  
Singular Point ◽  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Subdivision Scheme ◽  
Fractal Curve ◽  
Rational Scheme ◽  
Special Cases ◽  
Necessary And Sufficient ◽  
Parameter Values ◽  
Selection Of

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan–Ivrissimtzis’s scheme, Siddiqi–Rehan’s scheme, and Siddiqi–Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

scholarly journals Global asymptotic stability of a passive juggling strategy: A possible parts-feeding method

1995 ◽  
Vol 1 (3) ◽  
pp. 193-224 ◽  
Author(s):  
P. J. Swanson ◽  
R. R. Burridge ◽  
D. E. Koditschek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Initial Conditions ◽  
Periodic Trajectory ◽  
Degree Of Freedom ◽  
Feeding Method ◽  
Feeding Problem ◽  
Simulation Results ◽  
Parts Feeding

In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.

Dynamic bifurcations in non-stationary systems: transitions with an unpredictable outcome

1995 ◽  
Vol 451 (1942) ◽  
pp. 471-485 ◽  
Keyword(s):  
Critical Parameter ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Important Concept ◽  
New Form ◽  
Parameter Values ◽  
Dynamic Bifurcations

In nonlinear non-stationary systems, dynamic bifurcations result in a transition to a qualitatively new state. In this paper we examine how the dynamics of transition of such systems may be assessed using the concept of transient basins of attraction. We delineate the phenomenon of indeterminate dynamic bifurcations, where it is shown that the response, after the system passes through critical parameter values, may be extremely sensitive to the choice of initial conditions or parameter states. This new form of unpredictability in systems whose parameters vary with time, is clearly an important concept to be assimilated in the theory of non-stationary dynamics.

FLUCTUATIONS IN THE STATE OF CHAOS-CHAOS INTERMITTENCY OF CHUA’S CIRCUIT

1995 ◽  
Vol 05 (01) ◽  
pp. 271-273
Author(s):  
M. KOCH ◽  
R. TETZLAFF ◽  
D. WOLF
Keyword(s):  
Power Spectrum ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
The State ◽  
Circuit Parameter ◽  
Chua’S Circuit ◽  
External Excitation ◽  
Chua's Circuit ◽  
Parameter Values

We studied the power spectrum of the normalized voltage across the capacitor parallel to a piecewise-linear resistor of Chua’s circuit in the “chaos-chaos intermittency” state [Anishchenko et al., 1992]. The investigations included various initial conditions and circuit parameter values without and with external excitation. In all cases we found spectra showing a 1/ω2-decay over more than four decades.

scholarly journals Topographically forced long waves on a sheared coastal current. Part 2. Finite amplitude waves

1997 ◽  
Vol 343 ◽  
pp. 153-168 ◽  
Author(s):  
S. R. CLARKE ◽  
E. R. JOHNSON
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Coastal Current ◽  
Constant Vorticity ◽  
Long Wave ◽  
Long Time ◽  
Wave Limit ◽  
Parameter Values ◽  
Upstream Flow

This paper analyses the finite-amplitude flow of a constant-vorticity current past coastal topography in the long-wave limit. A forced finite-amplitude long-wave equation is derived to describe the evolution of the vorticity interface. An analysis of this equation shows that three distinct near-critical regimes occur. In the first the upstream flow is restricted, with overturning of the vorticity interface for sufficiently large topography. In the second quasi-steady nonlinear waves form downstream of the topography with weak upstream influence. In the third regime the upstream rotational fluid is partially blocked. Blocking and overturning are enhanced at headlands with steep rear faces and decreased at headlands with steep forward faces. For certain parameter values both overturning and partially blocked solutions are possible and the long-time evolution is critically dependent on the initial conditions. The reduction of the problem to a one-dimensional nonlinear wave equation allows solutions to be followed to much longer times and parameter space to be explored more finely than in the related pioneering contour-dynamical integrations of Stern (1991).

Sign in / Sign up

Export Citation Format

Share Document