# Boundaries of Stability Domains for Equilibrium Points of Differential Equations with Parameters

## Abstract

We consider autonomous and periodic differential equations containing two scalar parameters and analyze the construction of boundaries of stability domains of equilibrium points for such equations in the plane of parameters. We indicate conditions under which a unique smooth boundary curve passes through a given point. We propose a scheme of approximate construction of this curve.

- Authors:

- Bashkir State University (Russian Federation)
- Bashkir State Agrarian University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771260

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DIAGRAMS; DIFFERENTIAL EQUATIONS; EQUILIBRIUM; PERIODICITY; SCALARS; STABILITY

### Citation Formats

```
Yumagulov, M. G., E-mail: yum-mg@mail.ru, Ibragimova, L. S., E-mail: lilibr@mail.ru, and Mustafina, I. Zh., E-mail: fanina84@bk.ru.
```*Boundaries of Stability Domains for Equilibrium Points of Differential Equations with Parameters*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3797-X.

```
Yumagulov, M. G., E-mail: yum-mg@mail.ru, Ibragimova, L. S., E-mail: lilibr@mail.ru, & Mustafina, I. Zh., E-mail: fanina84@bk.ru.
```*Boundaries of Stability Domains for Equilibrium Points of Differential Equations with Parameters*. United States. doi:10.1007/S10958-018-3797-X.

```
Yumagulov, M. G., E-mail: yum-mg@mail.ru, Ibragimova, L. S., E-mail: lilibr@mail.ru, and Mustafina, I. Zh., E-mail: fanina84@bk.ru. Tue .
"Boundaries of Stability Domains for Equilibrium Points of Differential Equations with Parameters". United States. doi:10.1007/S10958-018-3797-X.
```

```
@article{osti_22771260,
```

title = {Boundaries of Stability Domains for Equilibrium Points of Differential Equations with Parameters},

author = {Yumagulov, M. G., E-mail: yum-mg@mail.ru and Ibragimova, L. S., E-mail: lilibr@mail.ru and Mustafina, I. Zh., E-mail: fanina84@bk.ru},

abstractNote = {We consider autonomous and periodic differential equations containing two scalar parameters and analyze the construction of boundaries of stability domains of equilibrium points for such equations in the plane of parameters. We indicate conditions under which a unique smooth boundary curve passes through a given point. We propose a scheme of approximate construction of this curve.},

doi = {10.1007/S10958-018-3797-X},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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