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Related papers: Stereographically conjugate differential systems

200 papers

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…

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

The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…

Classical Analysis and ODEs · Mathematics 2009-11-17 D. Barrios Rolanía A. Branquinho A. Foulquié Moreno

General properties of the effective conductivity sigma_e of planar isotropic randomly inhomogeneous two-phase self-dual systems are investigated. A new approach for finding out sigma_e of random systems based on a duality, a series…

Disordered Systems and Neural Networks · Physics 2007-05-23 S. A. Bulgadaev

Following the previous authors works (joint with I.A.Dynnikov) we develop a theory of the discrete analogs of the differential-geometrical (DG) connections in the triangulated manifolds. We study a nonstandard discretization based on the…

Mathematical Physics · Physics 2007-05-23 S. P. Novikov

"Strange" correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states.…

Strongly Correlated Electrons · Physics 2023-07-07 Luca Lepori , Michele Burrello , Andrea Trombettoni , Simone Paganelli

We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical…

Analysis of PDEs · Mathematics 2008-09-22 Walter H. Aschbacher , Marco Squassina

The system of coupled discrete equations describing a two-component superlattice with interlaced linear and nonlinear constituents is revisited as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among…

Pattern Formation and Solitons · Physics 2009-11-13 Kyriakos Hizanidis , Yannis Kominis , Nikolaos K. Efremidis

Discrete arrays of Josephson junction elements differ from their continuum counterparts in two essential ways: i) localized dynamic states in discrete arrays, which are not present in the corresponding continuum system, can interact with…

chao-dyn · Physics 2008-02-03 R. D. Parmentier

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Pattern Formation and Solitons · Physics 2013-05-29 V. N. Biktashev , M. A. Tsyganov

In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor…

Pattern Formation and Solitons · Physics 2024-06-19 Arnab Mondal , Argha Mondal , M. A. Aziz-Alaoui , Ranjit Kumar Upadhyay , Sanjeev Kumar Sharma , Chris G. Antonopoulos

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

Chaotic Dynamics · Physics 2015-05-19 Srinivas Gorur Shandilya , Marc Timme

We investigate a new class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled while phase elements are…

The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…

Adaptation and Self-Organizing Systems · Physics 2022-02-24 Basma Khelfa , Raphael Korbmacher , Andreas Schadschneider , Antoine Tordeux

This paper is a step towards the complete topological classification of {\Omega}-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions for two such diffeomorphisms to be topologically…

Dynamical Systems · Mathematics 2016-08-02 V. Z. Grines , O. V. Pochinka , S. Van Strien

The distance matrix of a connected graph is defined as the matrix in which the entries are the pairwise distances between vertices. The distance spectrum of a graph is the set of eigenvalues of its distance matrix. A graph is said to be…

Combinatorics · Mathematics 2022-01-10 Anuj Sakarda , Jerry Tan , Armaan Tipirneni

For spinful systems with spin 1/2, it is generally believed that P and T invariant strong and second-order topologies exist in four band and eight band system, respectively. Here, by using periodic driving, we find it is possible to have…

Mesoscale and Nanoscale Physics · Physics 2024-06-14 Hong Wu , Yu-Chen Dong , Hui Liu

This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…

Differential Geometry · Mathematics 2012-03-23 W. Sarlet , G. Waeyaert

For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…

Dynamical Systems · Mathematics 2015-09-30 Miriam Manoel , Mark Roberts

The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…

Pattern Formation and Solitons · Physics 2022-11-30 Leonhard Schülen , Maria Mikhailenko , Everton S. Medeiros , Anna Zakharova