{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T08:32:43Z","timestamp":1765355563953,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,4,6]],"date-time":"2011-04-06T00:00:00Z","timestamp":1302048000000},"content-version":"vor","delay-in-days":95,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (non)chaotic dynamics. In this paper we consider homogeneous quadratic systems via the so\u2010called Markus approach. We use the one\u2010to\u2010one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960). We resume some connections between the dynamics of the quadratic systems and (algebraic) properties of the corresponding algebras. We consider some general connections and the influence of power\u2010associativity in the corresponding quadratic system.<\/jats:p>","DOI":"10.1155\/2011\/230939","type":"journal-article","created":{"date-parts":[[2011,4,6]],"date-time":"2011-04-06T19:33:11Z","timestamp":1302118391000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Algebraic Approach in Quadratic Systems"],"prefix":"10.1155","volume":"2011","author":[{"given":"Matej","family":"Mencinger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,4,6]]},"reference":[{"key":"e_1_2_4_1_2","doi-asserted-by":"crossref","DOI":"10.1155\/2010\/539087","article-title":"Stability of nonlinear autonomous quadratic discrete systems in the critical case","volume":"2010","author":"Dibl\u00edk J.","year":"2010","journal-title":"Discrete Dynamics in Nature and Society"},{"key":"e_1_2_4_2_2","first-page":"185","volume-title":"Annals of Mathematics Studies","author":"Markus L.","year":"1960"},{"key":"e_1_2_4_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091501000281"},{"key":"e_1_2_4_4_2","series-title":"Universitext","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8732-7","volume-title":"A First Course in Discrete Dynamical Systems","author":"Holmgren R. 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