Existence and stability of regularized shock solutions, with applications to rimming flows

2008 ◽  
Vol 63 (2-4) ◽  
pp. 197-212 ◽  
Author(s):  
E. S. Benilov ◽  
M. S. Benilov ◽  
S. B. G. O’Brien
Keyword(s):  
Existence And Stability ◽  
Rimming Flows

scholarly journals NATURAL SELECTION WITH NUCLEAR AND CYTOPLASMIC TRANSMISSION. I. A DETERMINISTIC MODEL

Genetics ◽  
1984 ◽  
Vol 107 (4) ◽  
pp. 679-701
Author(s):  
Andrew G Clark
Keyword(s):  
Natural Selection ◽  
General Model ◽  
Deterministic Model ◽  
Genetic Locus ◽  
Nuclear Genes ◽  
Stability Of Equilibria ◽  
Extensive Variation ◽  
Existence And Stability

ABSTRACT A deterministic model allowing variation at a nuclear genetic locus in a population segregating two cytoplasmic types is formulated. Additive, multiplicative and symmetric viability matrices are analyzed for existence and stability of equilibria. The protectedness of polymorphisms in both nuclear genes and cytoplasmic types is also investigated in the general model. In no case is a complete polymorphism protected with this deterministic model. Results are discussed in light of the extensive variation in mtDNA that has recently been reported.

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

Gap solitons supported by an optical lattice in biased photorefractive crystals having both the linear and quadratic electro-optic effect

2020 ◽  
Vol 75 (8) ◽  
pp. 749-756
Author(s):  
Aavishkar Katti ◽  
Chittaranjan P. Katti
Keyword(s):  
Band Gap ◽  
Optical Lattice ◽  
Propagation Constant ◽  
Gap Soliton ◽  
Electro Optic ◽  
Quadratic Nonlinearities ◽  
Existence And Stability ◽  
Gap Solitons ◽  
Finite Band ◽  
First Time

AbstractWe investigate the existence and stability of gap solitons supported by an optical lattice in biased photorefractive (PR) crystals having both the linear and quadratic electro-optic effect. Such PR crystals have an interesting interplay between the linear and quadratic nonlinearities. Gap solitons are predicted for the first time in such novel PR media. Taking a relevant example (PMN-0.33PT), we find that the gap solitons in the first finite bandgap are single humped, positive and symmetric solitons while those in the second finite band gap are antisymmetric and double humped. The power of the gap soliton depends upon the value of the axial propagation constant. We delineate three power regimes and study the gap soliton profiles in each region. The gap solitons in the first finite band gap are not linearly stable while those in the second finite band gap are found to be stable against small perturbations. We study their stability properties in detail throughout the finite band gaps. The interplay between the linear and quadratic electro-optic effect is studied by investigating the spatial profiles and stability of the gap solitons for different ratios of the linear and quadratic nonlinear coefficients.

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