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1.
Stability analysis of the singular points and Hopf bifurcations of a tumor growth control model
Dániel 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
.pdf Celotno besedilo (2,44 MB)

2.
Qualitative study of a well-stirred isothermal reaction model
Barbara Arcet, Maša Dukarić, Zhibek Kadyrsizova, 2020, izvirni znanstveni članek

Opis: We consider a two-dimensional system which is a mathematical model for a temporal evolution of a well-stirred isothermal reaction system. We give sufficient conditions for the existence of purely imaginary eigenvalues of the Jacobian matrix of the system at its fixed points. Moreover, we show that the system admits a supercritical Hopf bifurcation.
Ključne besede: limit cycle, Hopf bifurcation, stability, reaction kinetics
Objavljeno v DKUM: 16.10.2023; Ogledov: 329; Prenosov: 35
.pdf Celotno besedilo (516,87 KB)
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3.
Limit cycle bifurcated from a center in a three dimensional system
Bo 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
.pdf Celotno besedilo (236,33 KB)
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4.
Bifurcations of planar Hamiltonian systems with impulsive perturbation
Zhaoping 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
URL Povezava na celotno besedilo

5.
Limit cycle bifurcations from a nilpotent focus or center of planar systems
Maoan Han, Valery Romanovski, 2012, izvirni znanstveni članek

Opis: We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.
Ključne besede: mathematic, limit cycles, bifurcation, center problem
Objavljeno v DKUM: 10.07.2015; Ogledov: 1259; Prenosov: 350
.pdf Celotno besedilo (1,95 MB)
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6.
The study of isochronicity and critical period bifurcations on center manifolds of 3-dim polynomial systems using computer algebra
Matej Mencinger, Brigita Ferčec, 2013, objavljeni znanstveni prispevek na konferenci

Opis: Using the solution of the center-focus problem from [4], we present the investigation of isochronicity and critical period bifurcations of two families of cubic 3-dim systems of ODEs. Both cubic systems have a center manifold filled with closed trajectories. The presented study is performed using computer algebra systems Mathematica and Singular.
Ključne besede: polynomial systems of ODEs, center manifolds, isochronicity, bifurcation of critical periods, CAS
Objavljeno v DKUM: 10.07.2015; Ogledov: 1552; Prenosov: 65
URL Povezava na celotno besedilo

7.
Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems
Marko 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
URL Povezava na celotno besedilo
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8.
Estimating the number of limit cycles in polynomials systems
Maoan Han, Valery Romanovski, 2010, izvirni znanstveni članek

Opis: We describe a method based on algorithms of computational algebra for obtaining an upper bound for the number of limit cycles bifurcating from a center or a focus of polynomial vector field. We apply it to a cubic system depending on six parameters and prove that in the generic case at most six limit cycles can bifurcate from any center or focus at the origin of the system.
Ključne besede: mathematics, limit cycles, bifurcation
Objavljeno v DKUM: 07.06.2012; Ogledov: 1514; Prenosov: 124
URL Povezava na celotno besedilo

9.
Limit cycle bifurcations of some Liénard sytems
Yunmin Yang, Maoan Han, Valery Romanovski, 2010, izvirni znanstveni članek

Opis: In this paper we first give some general theorems on the limit cycle bifurcation for near-Hamiltonian systems near a double homoclinic loop or a center as a preliminary. Then we use these theorems to study some polynomial Liénard systems with perturbations and give new lower bounds for the maximal number of limit cycles of these systems.
Ključne besede: mathematics, bifurcation
Objavljeno v DKUM: 07.06.2012; Ogledov: 1422; Prenosov: 47
URL Povezava na celotno besedilo

10.
Symmetry breaking phenomena of purely viscous shear-thinning fluid flow in a locally constricted channel
Primož 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
URL Povezava na celotno besedilo

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