1. Stability analysis of the singular points and Hopf bifurcations of a tumor growth control modelDániel András Drexler, Ilona Nagy, Valery Romanovski, 2024, izvirni znanstveni članek Opis: We carry out qualitative analysis of a fourth-order tumor growth control model using ordinary differential equations. We show that the system has one positive equilibrium point, and its stability is independent of the feedback gain. Using a Lyapunov function method, we prove that there exist realistic parameter values for which the systems admit limit cycle oscillations due to a supercritical Hopf bifurcation. The time evolution of the state variables is also represented.
Ključne besede: bifurcation, cancer therapy, limit cycle, singular point, tumor therapy, tumor control
Objavljeno v DKUM: 12.08.2024; Ogledov: 73; Prenosov: 9
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3. Limit cycle bifurcated from a center in a three dimensional systemBo Sang, Brigita Ferčec, Qin-Long Wang, 2016, izvirni znanstveni članek Opis: Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $Є^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al). It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.
Ključne besede: algorithms, three dimensional systems, focal value, limit cycle, Hopf bifurcation, center
Objavljeno v DKUM: 08.08.2017; Ogledov: 2707; Prenosov: 144
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4. Bifurcations of planar Hamiltonian systems with impulsive perturbationZhaoping Hu, Maoan Han, Valery Romanovski, 2013, izvirni znanstveni članek Opis: In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under which a harmonic or subharmonic solution exists.
Ključne besede: matematika, Hamiltonski sistemi, diferencialne enačbe, bifurkacija, mathematics, Hamiltonian systems, differential equations, bifurcation
Objavljeno v DKUM: 10.07.2015; Ogledov: 1540; Prenosov: 103
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7. Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systemsMarko Gosak, Matjaž Perc, 2007, izvirni znanstveni članek Opis: We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems. We attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments.
Ključne besede: chaotic systems, spatial resonance, coherence resonance, nonlinear systems, noise, spatial dynamics, mathematical models, bifurcation diagrame
Objavljeno v DKUM: 07.06.2012; Ogledov: 2407; Prenosov: 143
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10. Symmetry breaking phenomena of purely viscous shear-thinning fluid flow in a locally constricted channelPrimož Ternik, 2008, izvirni znanstveni članek Opis: The goal of a present study is to investigate the effects of generalized Newtonian fluids on the threshold of the transition from flow symmetry to its asymmetry for the flow through a locally constricted channel. We consider purely viscous shear-thinning fluid and compare it with the Newtonian fluid. Fluid flow is studied numerically by solving the two dimensional momentum equations along with the continuity equation and the Carreau-Yasuda rheological model. We report systematic results in a range of generalized Reynolds number 250▫$leq$▫Re▫$leq$▫150 with a focus on its critical value. Results indicate that the shear-thinning viscous behaviour decreases the onset of bifurcation phenomena and the critical value of Reynolds number. Last but not least, a systematic grid refinement analysis and numerical accuracy study is performed and present numerical results may be treated as the benchmark.
Ključne besede: bifurcation, inelastic shear-thinning fluid, Carreau-Yasuda model, numerical modelling
Objavljeno v DKUM: 31.05.2012; Ogledov: 2040; Prenosov: 143
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