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Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
The original continuous-time "goldfish" dynamical system is characterized by two neat formulas, the first of which provides the $N$ Newtonian equations of motion of this dynamical system, while the second provides the solution of the…
S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper…
We study dynamical systems arising from word maps on simple groups. We develop a geometric method based on the classical trace map for investigating periodic points of such systems. These results lead to a new approach to the search of…
The article take up two-dimensional subalgebras from optimum system of algebra $L_{13}$, which is deduce from the gas dynamics equations. We calculated invariants and constructed invariant submodels for two-dimensional sabalgebras. Then…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
Relations between points in the phase space are central to the study of topological dynamical systems. Since many of these relations share common properties, it is natural to study them within a unified framework. To this end, we introduce…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
By taking a product of two sl(2) representations, we obtain the differential operators preserving some space of polynomials in two variables. This allows us to construct the representations of osp(2,2) in terms of matrix differential…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
The relationship between two dynamical systems, one of which is obtained from the other by forming the quotient by an action of an involution commuting with the dynamics, is studied. The constraints and the possible extent of freedom in the…
In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…