The Existence and Stability of Asymmetric Spike Patterns for the Schnakenberg Model

2002 ◽  
Vol 109 (3) ◽  
pp. 229-264 ◽  
Author(s):  
Michael J. Ward ◽  
Juncheng Wei
Keyword(s):  
Schnakenberg Model ◽  
Existence And Stability ◽  
Spike Patterns

The Existence and Stability of Spike Patterns in a Chemotaxis Model

2005 ◽  
Vol 65 (3) ◽  
pp. 790-817 ◽  
Author(s):  
B. D. Sleeman ◽  
Michael J. Ward ◽  
J. C. Wei
Keyword(s):  
Chemotaxis Model ◽  
Existence And Stability ◽  
Spike Patterns

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.

Sign in / Sign up

Export Citation Format

Share Document