Local stability conditions in fluid dynamics

1991 ◽  
Vol 3 (11) ◽  
pp. 2644-2651 ◽  
Author(s):  
Alexander Lifschitz ◽  
Eliezer Hameiri
Keyword(s):  
Fluid Dynamics ◽  
Local Stability ◽  
Stability Conditions

scholarly journals Enhancing synchrony in multiplex network due to rewiring frequency

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190460 ◽  
Author(s):  
Sarbendu Rakshit ◽  
Bidesh K. Bera ◽  
Jürgen Kurths ◽  
Dibakar Ghosh
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Lorenz System ◽  
Stability Conditions ◽  
Network Architectures ◽  
Stability Function ◽  
Individual Layer ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Different Types

Most of the previous studies on synchrony in multiplex networks have been investigated using different types of intralayer network architectures which are either static or temporal. Effect of a temporal layer on intralayer synchrony in a multilayered network still remains elusive. In this paper, we discuss intralayer synchrony in a multiplex network consisting of static and temporal layers and how a temporal layer influences other static layers to enhance synchrony simultaneously. We analytically derive local stability conditions for intralayer synchrony based on the master stability function approach. The analytically derived results are illustrated by numerical simulations on up to five-layers multiplex networks with the paradigmatic Lorenz system as the node dynamics in each individual layer.

Dynamic analysis of a fractional order system

2015 ◽  
Vol 08 (06) ◽  
pp. 1550079
Author(s):  
M. Javidi ◽  
N. Nyamoradi
Keyword(s):  
Stability Analysis ◽  
Fractional Derivative ◽  
Dynamic Analysis ◽  
Fractional Order ◽  
Local Stability ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Order System ◽  
Stability Conditions ◽  
Hurwitz Stability

In this paper, we investigate the dynamical behavior of a fractional order phytoplankton–zooplankton system. In this paper, stability analysis of the phytoplankton–zooplankton model (PZM) is studied by using the fractional Routh–Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.

Stability Conditions for a Class of Distributed-Parameter Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 475-479 ◽  
Author(s):  
R. E. Blodgett
Keyword(s):  
Equilibrium State ◽  
Local Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Chemical Reactor ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Stability Conditions ◽  
Stability And Instability ◽  
Liapunov's Direct Method

The purpose of this paper is to obtain stability conditions for a class of nonlinear distributed-parameter systems by using a generalization of Liapunov’s direct method. Sufficient conditions for local stability and instability of the equilibrium state are derived. An application is given in which conditions are obtained for stability of a chemical-reactor process.

scholarly journals The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect

2021 ◽  
pp. 3114-3127
Author(s):  
Saad M. A. Al-Momen ◽  
Raid Kamil Naji
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Allee Effect ◽  
Pitchfork Bifurcation ◽  
Stability Conditions ◽  
Analytical Results ◽  
Saddle Node ◽  
Strong Allee Effect ◽  
Predator Model

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

A fractional-order toxin producing phytoplankton and zooplankton system

2014 ◽  
Vol 07 (04) ◽  
pp. 1450039 ◽  
Author(s):  
M. Javidi ◽  
N. Nyamoradi
Keyword(s):  
Stability Analysis ◽  
Nutrient Cycling ◽  
Fractional Order ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Stability Conditions ◽  
Hurwitz Stability ◽  
Local Stability Analysis ◽  
Mathematical System ◽  
Parameter Values

In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton–zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh–Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.

scholarly journals Local stability conditions for discrete-time cascade locally recurrent neural networks

2010 ◽  
Vol 20 (1) ◽  
pp. 23-34 ◽  
Author(s):  
Krzysztof Patan
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Local Stability ◽  
Learning Problems ◽  
Stability Conditions ◽  
Neuron Models ◽  
Optimization Task ◽  
Dynamic Type ◽  
Locally Recurrent

Local stability conditions for discrete-time cascade locally recurrent neural networksThe paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem, a gradient projection method is adopted. The efficiency and usefulness of the proposed approach are justified by using a number of experiments.

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