Phase portraits and bifurcation diagram of the Gray-Scott model
نویسندگان
چکیده
We give a complete classification of the phase portraits in Poincare´ disk for cubic polynomial systemsx˙=1−x−axy2,y˙=−by+axy2, R2 according with values its two parameters and b. These differential systems correspond to Gray-Scott model. Moreover we provide bifurcation diagram parameter plane (a,b) these systems.
منابع مشابه
The Static bifurcation Diagram for the Gray-Scott Model
Gray, Scott and their collaborators proposed the model analyzed in our paper in the 80’s. The model describes an autocatalytic mechanism in isothermal systems where the reaction rate is increased by strengthening the concentration of one of the products. The chemical reaction (Fig. 1) occurs in a continuously stirred tank reactor (CSTR) and it involves two reactants X and Y with concentrations ...
متن کاملGray - Scott Model
In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k 1 ; k 2 , there are asymmetric solutions with k 1 large spots (type A) and k 2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetr...
متن کاملSpike autosolitons in the Gray-Scott model
We performed a comprehensive study of the spike autosolitons: self-sustained solitary inhomogeneous states, in the classical reaction-diffusion system — the GrayScott model. We developed singular perturbation techniques based on the strong separation of the length scales to construct asymptotically the solutions in the form of a one-dimensional static autosolitons, higher-dimensional radially-s...
متن کاملSpike autosolitons in Gray-Scott model
We performed a comprehensive study of spike autosolitons: highly localized solitary states, in the classical reaction-diffusion system — the Gray-Scott model. We developed singular perturbation techniques based on the strong separation of length scales to construct asymptotically the solutions in the form of one-dimensional and higher-dimensional radially-symmetric static autosolitons, and two ...
متن کاملControl of spatiotemporal patterns in the Gray-Scott model.
This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species, diagonal, and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from traveling waves. In the case of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2021
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2020.124840