Nonlinear Sciences
New submissions
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New submissions for Fri, 23 Aug 19
 [1] arXiv:1908.08274 [pdf, other]

Title: Invasion Fronts Outside the Homoclinic Snaking Region in the Planar SwiftHohenberg EquationAuthors: David J.B. LloydComments: 42 pages, 22 figuresSubjects: Pattern Formation and Solitons (nlin.PS); Dynamical Systems (math.DS)
In this paper, we carry out numerical bifurcation analysis of depinning of fronts near the homoclinic snaking region, involving a spatial stripe cellular pattern embedded in a quiescent state, in the twodimensional SwiftHohenberg equation with either a quadraticcubic or cubicquintic nonlinearity. We focus on depinning fronts involving stripes that are orientated either parallel, oblique and perpendicular to the front interface, and almost planar depinning fronts. We show that invading parallel depinning fronts select both a farfield wavenumber and a propagation wavespeed whereas retreating parallel depinning fronts come in families where the wavespeed is a function of the farfield wavenumber. Employing a farfield core decomposition, we propose a boundary value problem for the invading depinning fronts which we numerically solve and use pathfollowing routines to trace out bifurcation diagrams. We then carry out a thorough numerical investigation of the parallel, oblique, perpendicular stripe, and almost planar invasion fronts. We find that almost planar invasion fronts in the cubicquintic SwiftHohenberg equation bifurcate off parallel invasion fronts and coexist close to the homoclinic snaking region. Sufficiently far from the 1D homoclinic snaking region, no almost planar invasion fronts exist and we find that parallel invasion stripe fronts may regain transverse stability if they propagate above a critical speed. Finally, we show that depinning fronts shed light on the time simulations of fully localised patches of stripes on the plane. The numerical algorithms detailed have wider application to general modulated fronts and reactiondiffusion systems.
 [2] arXiv:1908.08470 [pdf, other]

Title: Nests and Chains of Hofstadter ButterfliesSubjects: Chaotic Dynamics (nlin.CD); Quantum Gases (condmat.quantgas)
The \lq Hofstadter butterfly', a plot of the spectrum of an electron in a twodimensional periodic potential with a uniform magnetic field, contains subsets which resemble small, distorted images of the entire plot. We show how the sizes of these subimages are determined, and calculate scaling factors describing their selfsimilar nesting, revealing an unexpected simplicity in the fractal structure of the spectrum. We also characterise semiinfinite chains of subimages, showing one end of the chain is a result of gap closure, and the other end is at an accumulation point.
Crosslists for Fri, 23 Aug 19
 [3] arXiv:1908.08105 (crosslist from condmat.disnn) [pdf, other]

Title: Memristive Networks: from Graph Theory to Statistical PhysicsComments: 7 pages double columns; invited EPL Perspectives paperSubjects: Disordered Systems and Neural Networks (condmat.disnn); Statistical Mechanics (condmat.statmech); Adaptation and SelfOrganizing Systems (nlin.AO)
We provide an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.
 [4] arXiv:1908.08134 (crosslist from quantph) [pdf, other]

Title: Quantum NeimarkSacker bifurcationComments: 7 pages, 6 figuresSubjects: Quantum Physics (quantph); Chaotic Dynamics (nlin.CD)
Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddlenode, and period doubling classical bifurcations. Here, making use of the periodically modulated open quantum dimer model, we report and investigate a quantum NeimarkSacker bifurcation. Its classical counterpart is the birth of a torus (an invariant curve in the Poincar\'{e} section) due to instability of a limit cycle (fixed point of the Poincar\'{e} map). The quantum system exhibits a transition from unimodal to bagel shaped stroboscopic distributions, as for Husimi representation, as for observables. The spectral properties of Floquet map experience changes reminiscent of the classical case, a pair of complex conjugated eigenvalues approaching a unit circle. Quantum MonteCarlo wave function unraveling of the Lindblad master equation yields dynamics of single trajectories on "quantum torus" and allows for quantifying it by rotation number. The bifurcation is sensitive to the number of quantum particles that can also be regarded as a control parameter.
 [5] arXiv:1908.08325 (crosslist from qbio.CB) [pdf, other]

Title: Modelling physical limits of migration by a kinetic model with nonlocal sensingSubjects: Cell Behavior (qbio.CB); Adaptation and SelfOrganizing Systems (nlin.AO)
Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell overcrowding may hamper cells from moving in certain directions or even from sensing beyond regions that practically act like physical barriers. We extend the nonlocal kinetic model proposed by Loy and Preziosi (2019) to include situations in which the sensing radius is not constant, but depends on position, sensing direction and time as cells' behavior might be determined on the basis of information collected before reaching physically limiting configurations. We analyze how the actual possible sensing of the environment influences the dynamics by recovering the appropriate macroscopic limits and by integrating numerically the kinetic transport equation.
Replacements for Fri, 23 Aug 19
 [6] arXiv:1710.04522 (replaced) [pdf, ps, other]

Title: Haantjes Algebras and DiagonalizationComments: 27 pages, no figuresSubjects: Mathematical Physics (mathph); Differential Geometry (math.DG); Operator Algebras (math.OA); Exactly Solvable and Integrable Systems (nlin.SI)
 [7] arXiv:1810.01444 (replaced) [pdf, other]
 [8] arXiv:1810.11474 (replaced) [pdf, other]

Title: Generating MultiScroll Chua's Attractors via Simplified PiecewiseLinear Chua's DiodeComments: 14 pages, 15 figuresJournalref: IEEE Transactions on Circuits and Systems I: Regular Papers, 2019Subjects: Chaotic Dynamics (nlin.CD); Signal Processing (eess.SP)
 [9] arXiv:1903.02690 (replaced) [pdf, other]

Title: Energy extraction of a chaotic system in a cyclic process: a Szilárd Engine perspectiveComments: 22 pages, 15 figuresJournalref: Soriani, A and Bonan\c{c}a, M V S, Energy extraction of a chaotic system in a cyclic process: a Szil\'ard engine perspective, J. Stat. Mech (2019) 083210Subjects: Statistical Mechanics (condmat.statmech); Chaotic Dynamics (nlin.CD)
 [10] arXiv:1903.10030 (replaced) [pdf, ps, other]

Title: On symmetries of generalized Calogero model and PolychronakosFrahm chainAuthors: Tigran HakobyanComments: 9 pagesJournalref: Phys. Rev. D 99, 105011 (2019)Subjects: High Energy Physics  Theory (hepth); Strongly Correlated Electrons (condmat.strel); Mathematical Physics (mathph); Exactly Solvable and Integrable Systems (nlin.SI)
 [11] arXiv:1905.04367 (replaced) [pdf, ps, other]

Title: Emergence of Subcritical Bifurcations in a System of Randomly Coupled Supercritical AndronovHopf Oscillators: A Potential Mechanism for Neural Network Type SwitchingSubjects: Dynamical Systems (math.DS); Adaptation and SelfOrganizing Systems (nlin.AO); Biological Physics (physics.bioph); Neurons and Cognition (qbio.NC)
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