scholarly journals Dynamical properties of a mutualism system in the presence of noise and time delay

2009 ◽  
Vol 39 (2) ◽  
Author(s):  
Chun-Hua Zeng ◽  
Gui-Qin Zhang ◽  
Xiao-Feng Zhou
Keyword(s):  
Time Delay ◽  
Dynamical Properties ◽  
Mutualism System

Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria

2011 ◽  
pp. 331-357 ◽  
Author(s):  
Daniela Danciu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Delay ◽  
Dynamical Systems ◽  
Qualitative Properties ◽  
The Neural Network ◽  
The Neural Networks ◽  
Global Asymptotics ◽  
Dynamical Properties

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.

scholarly journals Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yufeng Wang ◽  
Youhua Qian ◽  
Bingwen Lin
Keyword(s):  
Numerical Simulation ◽  
Perturbation Theory ◽  
Time Delay ◽  
Existence And Uniqueness ◽  
Relaxation Oscillation ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Relaxation Oscillations ◽  
Oscillation Cycle ◽  
Dynamical Properties

In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.

DYNAMICAL PROPERTIES OF AN ANTI-TUMOR CELL GROWTH SYSTEM IN THE PRESENCE OF DELAY AND CORRELATED NOISES

2009 ◽  
Vol 23 (13) ◽  
pp. 1651-1661 ◽  
Author(s):  
CHUN-HUA ZENG ◽  
CHONG-WEI XIE
Keyword(s):  
Relaxation Time ◽  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Small Time ◽  
Correlated Noise ◽  
Tumor Cell Growth ◽  
Stationary Probability Distribution ◽  
Growth System ◽  
Dynamical Properties

We study dynamical properties of an anti-tumor cell growth system in the presence of time delay and correlations between multiplicative and additive white noise. Using the small time delay approximation, the Novikov theorem and Fox approach, the stationary probability distribution (SPD) is obtained. Based on the SPD, the expressions of the normalized correlation function C(s) and the associated relaxation time Tc are derived by means of Stratonovich decoupling ansatz. Based on numerical computations, we find the following: (i) The SPD exhibits one-peak → two-peaks → one-peak phase transitions as the correlation intensity λ varies. (ii) The relaxation time Tc exhibits a one-peak structure for negatively correlated noise (λ<0), however for positively correlated noise (λ>0), the relaxation time Tc decreases monotonously. (iii) The effects of the delay time τ on Tc and C(s) are entirely the same for λ<0 and for λ>0, i.e. τ enhances the fluctuation decay of the population of tumor cells.

From the Oort cloud to Halley-type comets

1999 ◽  
Vol 173 ◽  
pp. 327-338 ◽  
Author(s):  
J.A. Fernández ◽  
T. Gallardo
Keyword(s):  
Total Population ◽  
Complex Function ◽  
Dynamical Evolution ◽  
Oort Cloud ◽  
Capture Process ◽  
Influx Rate ◽  
Short Period ◽  
Dynamical Properties ◽  
Orbital Periods ◽  
Probability Of Capture

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods &lt; 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq &lt;2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods &lt; 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.

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