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Phase Portraits of the Leslie-Gower System
In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species. We give the complete description of their...
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Analysis of Solutions of Some Multi-Term Fractional Bessel Equations
We construct the existence theory for generalized fractional Bessel differential equations and find the solutions in the form of fractional or...
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Hyers—Ulam Stability of Second-Order Linear Dynamic Equations on Time Scales
We investigate the Hyers—Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on...
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On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a0(x) + a1(x) y + a2(x) y2 + … + an(x) yn
In this paper we deal with differential equations of the form yy ′ = P ( x , y ) where y ′ = dy / dx and P ( x , y ) is a polynomial in the variables x and y of...
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On the Integrability of the Abel and of the Extended Liénard Equations
We present some exact integrability cases of the extended Liénard equation y ″ + f ( y )( y ′) n + k ( y )( y ′) m + g ( y ) y ′ + h ( y ) = 0, with n > 0 and m > 0...
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Linearization criteria for two-dimensional systems of third-order ordinary differential equations by complex approach
Linearization criteria for two-dimensional systems of second-order ordinary differential equations (ODEs) have been derived earlier using complex...
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Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics
This article is devoted to the results of phase topology research on a generalized mathematical model, which covers such two problems as the dynamics...
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On solutions of linear fractional differential equations and systems thereof
We derive exact solutions to classes of linear fractional differential equations and systems thereof expressed in terms of generalized Wright...
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GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems
Generalized Bäcklund–Darboux transformations (GBDTs) of discrete skew-selfadjoint Dirac systems have been successfully used for explicit solving of...
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Darboux polynomials, balances and Painlevé property
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of...
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Bifurcation Analysis of the Dynamics of Two Vortices in a Bose–Einstein Condensate. The Case of Intensities of Opposite Signs
This paper is concerned with a system two point vortices in a Bose–Einstein condensate enclosed in a trap. The Hamiltonian form of equations of...
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Riccati equations and cone curves in Minkowski 3-space
In this paper, using the representation formula of cone curves and solving the Riccati equations respected to the structure function of cone curve,...
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On the integrability conditions for a family of Liénard-type equations
We study a family of Liénard-type equations. Such equations are used for the description of various processes in physics, mechanics and biology and...
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The integrable case of Adler–van Moerbeke. Discriminant set and bifurcation diagram
The Adler–van Moerbeke integrable case of the Euler equations on the Lie algebra so (4) is investigated. For the L – A pair found by Reyman and...
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Bending of Timoshenko beam with effect of crack gap based on equivalent spring model
Considering the effect of crack gap, the bending deformation of the Timoshenko beam with switching cracks is studied. To represent a crack with gap...
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Analytic enclosure of the fundamental matrix solution
This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of...
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On the connection of the quadratic Lienard equation with an equation for the elliptic functions
The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential...
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The general traveling wave solutions of the Fisher type equations and some related problems
In this article, we introduce two recent results with respect to the integrality and exact solutions of the Fisher type equations and their...