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Related papers: Naimark-Sacker Bifurcations in Linearly Coupled Qu…

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We study the phenomenon of intermittency in inhomogeneous lattices of coupled map where inhomogeneity appears in the form of different values of map parameters at adjacent sites.The system exhibits spatiotemporal intermittency in various…

chao-dyn · Physics 2016-08-31 Ashutosh Sharma , Neelima Gupte

We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based…

Pattern Formation and Solitons · Physics 2025-10-15 Fatihcan M. Atay , Haibo Ruan

Explicit computational formulas for coefficients of the periodic normal forms of the three most complex codim 2 bifurcations of limit cycles with dimension of the center manifold equal to 4 or to 5 in generic autonomous ODEs are derived.…

Dynamical Systems · Mathematics 2012-10-24 Virginie De Witte , Willy Govaerts , Yuri A. Kuznetsov , Hil Meijer

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…

Chaotic Dynamics · Physics 2025-07-15 Tim Zolkin , Sergei Nagaitsev , Ivan Morozov , Sergei Kladov , Young-Kee Kim

Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated…

Quantum Physics · Physics 2019-08-23 Igor Yusipov , Mikhail Ivanchenko

We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…

Dynamical Systems · Mathematics 2015-09-02 Amadeu Delshams , Marina Gonchenko , Sergey Gonchenko

In this paper, we study the bifurcation of limit cycles in Lienard systems of the form dot(x)=y-F(x), dot(y)=-x, where F(x) is an odd polynomial that contains, in general, several free parameters. By using a method introduced in a previous…

chao-dyn · Physics 2009-10-30 Hector Giacomini , Sebastien Neukirch

We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…

Dynamical Systems · Mathematics 2024-08-30 Samuel Everett

We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…

Dynamical Systems · Mathematics 2011-12-20 Pau Rabassa , Angel Jorba , Joan Carles Tatjer

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their…

chao-dyn · Physics 2016-08-14 Wolfram Just

The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…

chao-dyn · Physics 2008-02-03 Mercè Ollé , Daniel Pfenniger

This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of…

This paper presents an analysis on the effects of floating-point arithmetic on the constructing bifurcation diagram of the quadratic map. More precisely, we are interested in showing the dependence of initial conditions to obtain some…

Signal Processing · Electrical Eng. & Systems 2017-11-29 Thalita E. Nazare , Erivelton G. Nepomuceno , Bruno P. O. Paiva

A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…

Chaotic Dynamics · Physics 2007-05-23 Daniele Fournier-Prunaret , Ricardo Lopez-Ruiz , Abdel-Kaddous Taha

We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…

Statistical Mechanics · Physics 2009-11-13 T. Pereira , M. S. Baptista , J. Kurths

We study critical orbits and bifurcations within the moduli space of quadratic rational maps on $\mathbb{P}^1$. We focus on the family of curves, $Per_1(\lambda)$ for $\lambda$ in $\mathbb{C}$, defined by the condition that each $f\in…

Dynamical Systems · Mathematics 2017-05-17 Laura DeMarco , Xiaoguang Wang , Hexi Ye

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset…

Chaotic Dynamics · Physics 2009-11-07 M. Brack , M. Mehta , K. Tanaka

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor…

Chaotic Dynamics · Physics 2015-05-19 Christian Guill , Benjamin Reichardt , Barbara Drossel , Wolfram Just

In this work we study numerically a lattice composed of two parameter single quartic maps with local diffusive coupling. We find large regions over the parameter space where the single quartic map is periodic and the coupled system is not…

chao-dyn · Physics 2007-05-23 L G Brunnet , J A C Gallas

We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…

Chaotic Dynamics · Physics 2015-05-27 Hassan F. El-Nashar , Hilda A. Cerdeira