Saddle-node bifurcation in the dynamic analysis of a national energy market

This article presents preliminary results of the mathematical analysis of a national energy market. The modeling of the studied system was made from causal relationships between the supply and demand of a national energy market, obtaining a system of ordinary differential equations of the first order of the electric power capacity in construction, the electric power capacity installed and the price of electricity in the market (Redondo et.al, 2018). In the dynamic analysis of the model, a saddle-node bifurcation was identified for the case in which the elasticity of the price with respect to the reserve margin is considered null, which allowed establishing two prospective scenarios of the system: absolute disappearance of the supply of electricity or tendency of growth of the supply to the attention of the demand of the market

Download Full-text

PERIODIC SOLUTIONS AND BIFURCATIONS OF FIRST-ORDER PERIODIC IMPULSIVE DIFFERENTIAL EQUATIONS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024281 ◽

2009 ◽

Vol 19 (08) ◽

pp. 2515-2530 ◽

Cited By ~ 3

Author(s):

ZHAOPING HU ◽

MAOAN HAN

Keyword(s):

Periodic Solution ◽

Differential Equations ◽

Periodic Solutions ◽

Impulsive Differential Equations ◽

Saddle Node Bifurcation ◽

First Order ◽

Double Period ◽

Saddle Node ◽

Stability And Bifurcation

In this paper, we use the method of displacement functions to study the existence, stability and bifurcation of periodic solutions of scalar periodic impulsive differential equations. We obtain some new and interesting results on saddle-node bifurcation and double-period bifurcation of periodic solution.

Download Full-text

Rate-Induced Tipping and Saddle-Node Bifurcation for Quadratic Differential Equations with Nonautonomous Asymptotic Dynamics

SIAM Journal on Applied Dynamical Systems ◽

10.1137/20m1339003 ◽

2021 ◽

Vol 20 (1) ◽

pp. 500-540

Author(s):

Iacopo P. Longo ◽

Carmen Nún͂ez ◽

Rafael Obaya ◽

Martin Rasmussen

Keyword(s):

Differential Equations ◽

Quadratic Differential ◽

Saddle Node Bifurcation ◽

Saddle Node ◽

Asymptotic Dynamics

Download Full-text

A Driving-Gear Dynamic Analysis

Materials Science Forum ◽

10.4028/www.scientific.net/msf.931.422 ◽

2018 ◽

Vol 931 ◽

pp. 422-427

Author(s):

Yevgeniy M. Kudryavtsev

Keyword(s):

Mathematical Model ◽

Differential Equations ◽

Dynamic Analysis ◽

Second Order ◽

New Approach ◽

First Order ◽

Gear Design ◽

Third Stage ◽

Mathcad Software ◽

High Level

A new approach of mechanical driving-gear dynamic analysis, which includes several modelling stages is observed in the article. On the first stage driving-gear is represented in the form of consistently connected rotation bodies. The driving-gear is represented in a graphic kind by means of the marked graph. On the second stage mathematical model of driving-gear performance with using of mnemonic rule is created. Mathematical model of mechanical driving-gear is a system of second-order regular differential equations (RDEs). The system of second-order regular differential equations is transformed into a system of first-order regular differential equations. There is a standard method for writing a higher-order RDE as a system of the first-order RDEs. On the third stage computer model of driving-gear performance using system Mathcad is created and initial data is defined. On the fourth stage the mechanical driving-gear modelling is performed and calculation data in numerical and graphical forms is obtained. This approach provides high level of the driving-gear dynamic analysis, including the received results presentation, which is especially important on the earliest stages of mechanical driving-gear design. The proposed procedure of mechanical driving-gear dynamic analysis using Mathcad software significantly decreases time and working costs on execution of such computations and helps to execute investigations related with changing of driving-gear elements parameters efficiently.

Download Full-text

A direct method for computing a closest saddle node bifurcation in the load power parameter space of an electric power system

1991., IEEE International Sympoisum on Circuits and Systems ◽

10.1109/iscas.1991.176181 ◽

2002 ◽

Cited By ~ 25

Author(s):

I. Dobson ◽

L. Lu ◽

Y. Hu

Keyword(s):

Power System ◽

Electric Power ◽

Parameter Space ◽

Direct Method ◽

Electric Power System ◽

Power Parameter ◽

Saddle Node Bifurcation ◽

Load Power ◽

Saddle Node ◽

A Direct Method

Download Full-text

A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN

Stochastics and Dynamics ◽

10.1142/s0219493704001103 ◽

2004 ◽

Vol 04 (03) ◽

pp. 335-350 ◽

Cited By ~ 14

Author(s):

ROBERTA FABBRI ◽

RUSSELL JOHNSON ◽

FRANCESCA MANTELLINI

Keyword(s):

Differential Equations ◽

Small Parameter ◽

Modern Theory ◽

Saddle Node Bifurcation ◽

Averaging Technique ◽

Saddle Node ◽

Nonautonomous Differential Equations ◽

Node Type

In this paper we study certain differential equations depending on a small parameter ε which exhibit a bifurcation of saddle-node type as ε passes through zero. We use a classical averaging technique together with methods and results from the modern theory of nonautonomous differential equations.

Download Full-text