scholarly journals A general model of size-dependent population dynamics with nonlinear growth rate

2004 ◽  
Vol 297 (1) ◽  
pp. 234-256 ◽  
Author(s):  
Nobuyuki Kato
Keyword(s):  
Growth Rate ◽  
Population Dynamics ◽  
General Model ◽  
Nonlinear Growth ◽  
Size Dependent

Some results for general cell-size-dependent branching processes

1973 ◽  
Vol 10 (2) ◽  
pp. 289-298 ◽  
Author(s):  
Aidan Sudbury ◽  
Peter Clifford
Keyword(s):  
Growth Rate ◽  
Cell Size ◽  
Wide Class ◽  
General Model ◽  
Branching Processes ◽  
Size Dependent ◽  
Sister Cells

A general model for the growth and division of cells in which the growth rate and division probability at any instant depend only on their size at that time is introduced. Conditions under which (a) the distribution of cell-size at division converges ergodically, (b) the sizes tend to 0 or ∞, are exhibited, and bounds to the correlation between the sizes at division of sister cells are given in a wide class of cases.

Some results for general cell-size-dependent branching processes

1973 ◽  
Vol 10 (02) ◽  
pp. 289-298
Author(s):  
Aidan Sudbury ◽  
Peter Clifford
Keyword(s):  
Growth Rate ◽  
Cell Size ◽  
Wide Class ◽  
General Model ◽  
Branching Processes ◽  
Size Dependent ◽  
Sister Cells

A general model for the growth and division of cells in which the growth rate and division probability at any instant depend only on their size at that time is introduced. Conditions under which (a) the distribution of cell-size at division converges ergodically, (b) the sizes tend to 0 or ∞, are exhibited, and bounds to the correlation between the sizes at division of sister cells are given in a wide class of cases.

scholarly journals Local existence for a general model of size-dependent population dynamics

1997 ◽  
Vol 2 (3-4) ◽  
pp. 207-226 ◽  
Author(s):  
Nobuyuki Kato ◽  
Hiroyuki Torikata
Keyword(s):  
Growth Rate ◽  
Population Dynamics ◽  
Initial Data ◽  
Continuous Dependence ◽  
Local Existence ◽  
Local Solution ◽  
Size Dependent ◽  
Structured Population ◽  
Structured Population Dynamics ◽  
Uniqueness Of The Solution

We shall investigate a size structured population dynamics with aging and birth functions having general forms. The growth rate we deal with depends not only on the size but also on time. We show the existence of a local solution and continuous dependence on the initial data, which shows the uniqueness of the solution as well.

Global Dynamics of a Holling-II Amensalism System with Nonlinear Growth Rate and Allee Effect on the First Species

2021 ◽  
Vol 31 (03) ◽  
pp. 2150050
Author(s):  
Demou Luo ◽  
Qiru Wang
Keyword(s):  
Growth Rate ◽  
Allee Effect ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Growth ◽  
Trivial Equilibrium ◽  
Existence And Stability ◽  
Stable Equilibria ◽  
Theoretical Results

Of concern is the global dynamics of a two-species Holling-II amensalism system with nonlinear growth rate. The existence and stability of trivial equilibrium, semi-trivial equilibria, interior equilibria and infinite singularity are studied. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, the global dynamics of the model is performed. Next, we incorporate Allee effect on the first species and offer a new analysis of equilibria and bifurcation discussion of the model. Finally, several numerical examples are performed to verify our theoretical results.

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