1. On the integrability of persistent quadratic three-dimensional systemsBrigita Ferčec, Maja Žulj, Matej Mencinger, 2024, original scientific article Abstract: 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.
Keywords: ordinary differential equations, three-dimensional systems, integrability problem, persistent systems
Published in DKUM: 23.05.2024; Views: 249; Downloads: 25
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2. 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, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, asimptotična stabilnost, mathematics, ordinary differential equations, neutral delay-differential system
Published in DKUM: 10.07.2015; Views: 1498; Downloads: 40
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3. 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, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, teorija operatorjev, funkcijska diferencialna enačba, teorija perturbacij, mathematics, ordinary differential equations, operator theory, functional differential equation, modulus semigroup, perturbation theory
Published in DKUM: 10.07.2015; Views: 1766; Downloads: 38
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4. 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, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, nelinearni funkcional, integro-diferencialna enačba, nevtralni tip, mathematics, ordinary differential equations, nonlinear functional, integro-differential equation, neutral type, mild solution
Published in DKUM: 10.07.2015; Views: 1065; Downloads: 27
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5. 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, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, Lotka-Volterrov sistem, stabilnost, funkcional Ljapunova, mathematics, ordinary differential equations, Lotka-Volterra system, Lyapunov functional, global asymptotic stability, infinite delays
Published in DKUM: 10.07.2015; Views: 1278; Downloads: 18
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6. 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, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, ▫$C_0$▫-polgrupe, stabilnost, mathematics, ordinary differential equations, ▫$C_0$▫-semigroups, uniform exponential stability
Published in DKUM: 10.07.2015; Views: 1135; Downloads: 37
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7. 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, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, ulomljene potence operatorjev, strukturni operatorji, mathematics, ordinary differential equations, fractional powers of operators, structural operators, abstract functional differential equations
Published in DKUM: 10.07.2015; Views: 1010; Downloads: 43
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8. 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, review, book review, critique Keywords: 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
Published in DKUM: 10.07.2015; Views: 1648; Downloads: 47
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