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Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder
We consider planar polynomial differential systems of degree 1 and 2 on the cylinder and we study their limit cycles. We prove that such linear...
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Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis
The paper presents a novel method that allows one to establish numerical solutions of linear and nonlinear ordinary differential equations—with...
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An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with Polynomial Nonlinearities
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations...
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A new framework for polynomial approximation to differential equations
In this paper, we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The...
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Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to...
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On a General Family of 2-Orthogonal Polynomial Eigenfunctions of a Third Order Differential Equation via Symbolic Computation
The search for 2-orthogonal polynomial eigenfunctions, with respect to a third order differential operator that does not increase the degree of...
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Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically,...
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Parameter Identification of Fractional Order Partial Differential Equation Model Based on Polynomial–Fourier Method
Parameter identification plays a crucial role in the study of dynamics for fractional order structural models. This article introduces an innovative...
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Limit Cycles of Discontinuous Piecewise Differential Systems Formed by Linear and Cubic Centers via Averaging Theory
Finding the number of limit cycles, as described by Poincaré (Memoire sur les coubes definies par une equation differentielle, Editions Jacques...
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Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application
The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytic Hamiltonian systems via the differential...
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Limit Cycles in Discontinuous Planar Piecewise Differential Systems with Multiple Nonlinear Switching Curves
In this paper, we investigate the maximum number of limit cycles that can bifurcate from the periodic annulus of the linear center for discontinuous...
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Qualitative dynamics of five quadratic polynomial differential systems exhibiting five classical cubic algebraic curves
This article is devoted to classify the dynamics of five quadratic differential systems exhibiting five known different cubic invariant algebraic...
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Equivalent Differential Equations in Problems of Control Theory and the Theory of Hamiltonian Systems
AbstractNew approaches are proposed in the problem of constructing equivalent scalar differential equations for multidimensional nonlinear systems...
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On the Exact Solutions of a Sequence of Nonlinear Differential Equations Possessing Polynomial Nonlinearities
We apply the Simple Equations Method (SEsM) to a sequence of nonlinear differential equations possessing polynomial nonlinearities and connected to...