Results 261 to 270 of about 24,699 (303)

Pitchfork bifurcation for non-autonomous interval maps

Journal of Difference Equations and Applications, 2009
In this work, we investigate attracting periodic orbits for non-autonomous discrete dynamical systems with two maps using a new approach. We study some types of bifurcation in these systems. We show that the pitchfork bifurcation plays an important role in the creation of attracting orbits in families of alternating systems with negative Schwarzian ...
D'ANIELLO, Emma, OLIVEIRA H.
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Stable Orbits and Bifurcation of Maps of the Interval

SIAM Journal on Applied Mathematics, 1978
Differentiable maps of class at least $C^3 $ from the unit interval to itself are shown to have a finite number of stable periodic orbits, each of which attracts the iterates of some critical point, assuming the hypothesis of everywhere negative Schwarzian derivative.
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Stability and bifurcations on a finite time interval in variational inequalities

Differential Equations, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kalinichenko, D. Yu., Reitmann, V., Skopinov, S. N.   +2 more
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Genealogy and Bifurcation Skeleton for Cycles of the Iterated Two-Extremum Map of the Interval

SIAM Journal on Mathematical Analysis, 1991
Dynamics of iterated maps of an interval with extrema is connected to the analysis of the parameter-plane curves that correspond to the existence of so-called superstable cycles (cycles that include a turning point of the map and hence have eigenvalue zero).
Ringland, J., Schell, M.
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Bifurcation and optimal harvesting of a diffusive predator–prey system with delays and interval biological parameters

Journal of Theoretical Biology, 2014
This paper deals with a delayed reaction-diffusion three-species Lotka-Volterra model with interval biological parameters and harvesting. Sufficient conditions for the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation.
Xuebing Zhang, Hongyong Zhao
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Homoclinic Ω-Explosion: Hyperbolicity Intervals and Their Bifurcation Boundaries

2015
It has been established by Gavrilov and Shilnikov (Math USSR Sb 17:467–485, 1972) that at the bifurcation boundary, separating Morse–Smale systems from systems with complicated dynamics, there are systems with homoclinic tangencies. Moreover, when crossing this boundary, infinitely many periodic orbits appear immediately, just by “explosion.” Newhouse ...
Sergey Gonchenko, Oleg Stenkin
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Bifurcation from interval and positive solutions for second order periodic boundary value problems

Applied Mathematics and Computation, 2010
Consider the periodic boundary value problem associated to the second order equation \[ u''-q(t)u+\lambda f(t,u) =0, \] where \(\lambda \geq 0,\) \(q\) is continuous, \(2\pi\)-periodic and non-negative and \(f\) is of class \({\mathcal C}^1\) and non-negative. The main hypothesis reads as follows: for suitable non-negative functions \(\xi_i, \eta_i\), \
Jia Xu, Ruyun Ma
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Period-Adding Bifurcation with Chaos in the Interspike Intervals Generated by an Experimental Neural Pacemaker

International Journal of Bifurcation and Chaos, 1997
The dynamics of the generation of the various spike trains in neural pacemakers is of fundamental importance to the understanding of neural coding. Recent studies have demonstrated, theoretically and experimentally, that neural pacemakers produce chaotic oscillations.
W. Ren, S. J. Hu, B. J. Zhang, F. Z. Wang, Y. F. Gong, J. X. Xu   +5 more
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Fixed-point bifurcation analysis in biological models using interval polynomials theory

Biological Cybernetics, 2014
The paper proposes a systematic method for fixed-point bifurcation analysis in circadian cells and similar biological models using interval polynomials theory. The stages for performing fixed-point bifurcation analysis in such biological systems comprise (i) the computation of fixed points as functions of the bifurcation parameter and (ii) the ...
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Bifurcation interval for positive solutions to discrete second-order boundary value problems

Journal of Difference Equations and Applications, 2011
Let be an integer with , , . We give a global description of the branches of positive solutions of the nonlinear eigenvalue problem which are not necessarily linearizable. Our approaches are based on topological degree and global bifurcation techniques.
Ruyun Ma, Chenghua Gao, Youji Xu
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