scholarly journals Stable Steady-State Solutions of Some Biological Aggregation Models

2021 ◽  
Vol 81 (3) ◽  
pp. 1248-1263
Author(s):  
Jonathan R. Potts ◽  
Kevin J. Painter
Keyword(s):  
Steady State ◽  
Stable Steady State ◽  
Steady State Solutions

Nonlinear Stability Considerations in Thermoelastic Contact

1999 ◽  
Vol 66 (1) ◽  
pp. 109-116 ◽  
Author(s):  
J. A. Pelesko
Keyword(s):  
Steady State ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Steady State Solution ◽  
Rigid Wall ◽  
Stable Steady State ◽  
Dynamic Information ◽  
Multiple Steady State ◽  
Singular Perturbation Technique ◽  
Steady State Solutions

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end a pressure and gap-dependent thermal boundary condition is imposed which couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using a two-timing or multiple-scale singular perturbation technique. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.

Transitions and instabilities of flow in a symmetric channel with a suddenly expanded and contracted part

2001 ◽  
Vol 434 ◽  
pp. 355-369 ◽  
Author(s):  
J. MIZUSHIMA ◽  
Y. SHIOTANI
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Nonlinear Stability ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Critical Conditions ◽  
Stable Steady State ◽  
Weakly Nonlinear ◽  
Symmetric Channel ◽  
Steady State Solutions

Transitions and instabilities of two-dimensional flow in a symmetric channel with a suddenly expanded and contracted part are investigated numerically by three different methods, i.e. the time marching method for dynamical equations, the SOR iterative method and the finite-element method for steady-state equations. Linear and weakly nonlinear stability theories are applied to the flow. The transitions are confirmed experimentally by flow visualizations. It is known that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number, regains the symmetry at another critical Reynolds number and becomes oscillatory at very large Reynolds numbers. Multiple stable steady-state solutions are found in some cases, which lead to a hysteresis. The critical conditions for the existence of the multiple stable steady-state solutions are determined numerically and compared with the results of the linear and weakly nonlinear stability analyses. An exchange of modes for oscillatory instabilities is found to occur in the flow as the aspect ratio, the ratio of the length of the expanded part to its width, is varied, and its relation with the impinging free-shear-layer instability (IFLSI) is discussed.

scholarly journals STABILITY ANALYSIS OF A LOTKA–VOLTERRA TYPE PREDATOR–PREY SYSTEM INVOLVING ALLEE EFFECTS

2010 ◽  
Vol 52 (2) ◽  
pp. 139-145 ◽  
Author(s):  
HÜSEYİN MERDAN
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Steady State Solution ◽  
Prey Population ◽  
Stable Steady State ◽  
Allee Effects ◽  
Predator Prey ◽  
Population Dynamics Model ◽  
Steady State Solutions ◽  
Model Subject

AbstractWe present a stability analysis of steady-state solutions of a continuous-time predator–prey population dynamics model subject to Allee effects on the prey population which occur at low population density. Numerical simulations show that the system subject to an Allee effect takes a much longer time to reach its stable steady-state solution. This result differs from that obtained for the discrete-time version of the same model.

Design of Circularly Towed Cable-Body Systems

2011 ◽  
Author(s):  
Varma Gottimukkala ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
Bifurcation Analysis ◽  
Small Diameter ◽  
The Body ◽  
Numerical Continuation ◽  
Stable Steady State ◽  
Dimensional System ◽  
Design Algorithm ◽  
Towed Cable ◽  
Steady State Solutions

Circularly towed cable-body systems can be used to pickup and deliver payloads, provide surveillance, and tow aerial and marine vehicles. To provide a stable operating platform, the body or end mass should have a unique and stable steady state solution with small diameter so that it travels at a much slower speed than the tow vehicle. In this paper, the minimum damping is calculated that ensures the stable single valued steady state solutions as a function of non-dimensional system parameters including cable length and end mass. Steady state solutions are found using the numerical continuation and bifurcation analysis and Galerkin’s method provides the linearized vibration equations that determine stability. Bifurcation analysis is also used to find the minimum achievable end mass radius. A design algorithm is presented and demonstrated using an example.

Nonlinear Stability, Thermoelastic Contact, and the Barber Condition

2000 ◽  
Vol 68 (1) ◽  
pp. 28-33 ◽  
Author(s):  
J. A. Pelesko
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Rigid Wall ◽  
Stable Steady State ◽  
Dynamic Information ◽  
Long Time ◽  
Uniform Expansions ◽  
Short Time ◽  
Matching Techniques ◽  
Steady State Solutions

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end we impose a pressure and gap-dependent thermal boundary condition. This condition, known as the Barber condition, couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using the asymptotic matching techniques of boundary layer theory to derive short-time, long-time, and uniform expansions. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.

Explicit steady state solutions for a particularM(x)/M/1 queueing system

1977 ◽  
Vol 24 (4) ◽  
pp. 651-659 ◽  
Author(s):  
George L. Jensen ◽  
Albert S. Paulson ◽  
Pasquale Sullo
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Steady State Solutions
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