Global Stability of the Positive Steady-State Solution of the Diffusion Holling-Tanner Model in a Heterogeneous Environment

2021 ◽  
Vol 11 (09) ◽  
pp. 1665-1672
Author(s):  
万红 张
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Steady State Solution ◽  
State Solution ◽  
Heterogeneous Environment ◽  
Positive Steady State

Steady-State Problem of an S-K-T Competition Model with Spatially Degenerate Coefficients

2021 ◽  
Vol 31 (11) ◽  
pp. 2150165
Author(s):  
Hao Zhou ◽  
Yu-Xia Wang
Keyword(s):  
Steady State ◽  
Global Bifurcation ◽  
Steady State Solution ◽  
Competition Model ◽  
State Solution ◽  
State Problem ◽  
Cross Diffusion ◽  
Positive Steady State ◽  
Steady State Problem ◽  
Steady State Solutions

In this paper, we study the steady-state problem of an S-K-T competition model with a spatially degenerate intraspecific competition coefficient. First, the global bifurcation continuum of positive steady-state solutions from its semitrivial steady-state solution is given, which depends on the spatial heterogeneity and cross-diffusion. Second, two limiting systems are derived as the cross-diffusion coefficient tends to infinity. Moreover, we demonstrate the existence of positive steady-state solutions near the two limiting systems, and show which one of the limiting systems characterizes the positive steady-state solution.

Spatial Patterns of a Predator–Prey Model with Beddington–DeAngelis Functional Response

2019 ◽  
Vol 29 (11) ◽  
pp. 1950145 ◽  
Author(s):  
Yu-Xia Wang ◽  
Wan-Tong Li
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Spatial Patterns ◽  
Bifurcation Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Positive Steady State ◽  
Prey System

This paper is concerned with the spatial patterns of a predator–prey system with Beddington–DeAngelis functional response, in which the parameter [Formula: see text] measuring the mutual interference between predators can play an essential role. By using the bifurcation theory and implicit function theorem we first consider the positive steady state solution bifurcating from the semitrivial steady state solution set of the system and prove that the positive steady state solution is constant. Then we show that nonconstant positive steady state solution may bifurcate from the constant positive steady state solution when [Formula: see text] is neither small nor large. Finally, we show that spatially nonhomogeneous periodic orbits may also bifurcate from the constant positive steady state solution as [Formula: see text] is not large.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

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