1. First integrals and invariants of systems of ordinary differential equationsMateja Grašič, Abdul Salam Jarrah, Valery Romanovski, 2025, izvirni znanstveni članek Opis: We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincaré-Dulac normal forms for autonomous systems of ordinary differential equations with a diagonal matrix of the linear part. Using tools from computational algebra, we develop an algorithmic approach for identifying generators of the algebras of monomial and polynomial first integrals, which works in the general case where the matrix of the linear part includes algebraic complex eigenvalues. Our method also provides a practical tool for exploring the algebraic structure of polynomial invariants and their relation to the Poincaré-Dulac normal forms of the underlying vector fields.
Ključne besede: first integrals, polynomial invariants, Poincaré-Dulac normal form, systems of ordinary differential equations
Objavljeno v DKUM: 27.11.2025; Ogledov: 0; Prenosov: 4
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2. On the integrability of persistent quadratic three-dimensional systemsBrigita Ferčec, Maja Žulj, Matej Mencinger, 2024, izvirni znanstveni članek Opis: We consider a nine-parameter familiy of 3D quadratic systems, �˙=�+�2(�,�,�), �˙=−�+�2(�,�,�), �˙=−�+�2(�,�,�), where �2,�2,�2 are quadratic polynomials, in terms of integrability. We find necessary and sufficient conditions for the existence of two independent first integrals of corresponding semi-persistent, weakly persistent, and persistent systems. Unlike some of the earlier works, which primarily focus on planar systems, our research covers three-dimensional spaces, offering new insights into the complex dynamics that are not typically apparent in lower dimensions.
Ključne besede: ordinary differential equations, three-dimensional systems, integrability problem, persistent systems
Objavljeno v DKUM: 23.05.2024; Ogledov: 249; Prenosov: 33
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3. Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan: Delay-dependent stability analysis for uncertain neutral systems with time-varying delays. (English). - [J] Math. Comput. Simul. 75, No. 1-2, 15-27 (2007). [ISSN 0378-4754]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, asimptotična stabilnost, mathematics, ordinary differential equations, neutral delay-differential system
Objavljeno v DKUM: 10.07.2015; Ogledov: 1498; Prenosov: 42
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4. Voigt, Jürgen: The modulus semigroup for linear delay equations II. (English). - [J] Note Mat. 25, No. 2, 191-208 (2006).[ISSN 1123-2536; ISSN 1590-0932]Miklavž Mastinšek, 2007, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, teorija operatorjev, funkcijska diferencialna enačba, teorija perturbacij, mathematics, ordinary differential equations, operator theory, functional differential equation, modulus semigroup, perturbation theory
Objavljeno v DKUM: 10.07.2015; Ogledov: 1766; Prenosov: 42
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5. Karunanithi, S.; Anthoni, S.M.: Existence of mild solutions of nonlinear functional integro-differential equations of neutral type. (English). - [CA] Sahadevan, R. (ed.) et al., Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14-16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House. 207-219 (2002). [ISBN 0-8493-1722-3; ISBN 81-7319-456-4]Miklavž Mastinšek, 2005, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, nelinearni funkcional, integro-diferencialna enačba, nevtralni tip, mathematics, ordinary differential equations, nonlinear functional, integro-differential equation, neutral type, mild solution
Objavljeno v DKUM: 10.07.2015; Ogledov: 1065; Prenosov: 29
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6. Xu, Rui; Chaplain, M. A. J.; Chen, Lansun: Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with infinite delays. -Appl. Math. Comput. 130, no. 2-3, 295-309 (2002). [ISSN 0096-3003]Miklavž Mastinšek, 2004, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, Lotka-Volterrov sistem, stabilnost, funkcional Ljapunova, mathematics, ordinary differential equations, Lotka-Volterra system, Lyapunov functional, global asymptotic stability, infinite delays
Objavljeno v DKUM: 10.07.2015; Ogledov: 1278; Prenosov: 20
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7. Megan, M.; Sasu, A. L.; Sasu, B.; Pogan, A.: Exponential stability and unstability of semigroups of linear operators in Banach spaces. - Math. Inequal. Appl. 5, no. 3, 557-567 (2002). [ISSN 1331-4343]Miklavž Mastinšek, 2004, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, ▫$C_0$▫-polgrupe, stabilnost, mathematics, ordinary differential equations, ▫$C_0$▫-semigroups, uniform exponential stability
Objavljeno v DKUM: 10.07.2015; Ogledov: 1135; Prenosov: 39
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8. Mastinšek, Miklavž: Structural operators for abstract functional differential equations. - Semigroup theory and applications, Proc. Conf. Trieste/Italy, Lect. Notes Pure Appl. Math. 116, 303-314 (1989)Miklavž Mastinšek, 1990, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, ulomljene potence operatorjev, strukturni operatorji, mathematics, ordinary differential equations, fractional powers of operators, structural operators, abstract functional differential equations
Objavljeno v DKUM: 10.07.2015; Ogledov: 1010; Prenosov: 45
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9. Arendt, Wolfgang; Bu, Shangquan: Tools for maximal regularity. - Math. Proc. Camb. Philos. Soc. 134, no. 2, 317-336 (2003). [ISSN 0305-0042; ISSN 1469-8064]Miklavž Mastinšek, 2004, recenzija, prikaz knjige, kritika Ključne besede: matematika, teorija operatorjev, navadne diferencialne enačbe, ▫$C_0$▫-polgrupe, maksimalna regularnost, nehomogeni Cauchyjev problem, mathematics, operator theory, ordinary differential equations, ▫$C_0$▫-semigroups, maximal regularity, inhomogeneous Cauchy problem, UMD-space, mild solution
Objavljeno v DKUM: 10.07.2015; Ogledov: 1648; Prenosov: 50
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