20 papers · ranked by Valyu relevance
Valentin Duruisseaux, A. R. Humphries
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of chaos. In particular a cusp bifurcation of periodic orbits and resulting branches…
Andrus Giraldo, Stefan Ruschel
We numerically investigate the branching of temporally localized, two-pulse periodic traveling waves from one-pulse periodic traveling waves with non-oscillating tails in delay differential equations (DDEs) with large delay. Solutions of this type are commonly referred to as temporal dissipative solitons (TDSs) [65] in…
Konstantinos Efstathiou, Tobias Våge Henriksen, Sonja Hohloch
In this paper we introduce a new bifurcation in Hamiltonian systems, which we call the double flip bifurcation. The Hamiltonian depends on two parameters, one of which controls the double flip bifurcation. The result of the bifurcation is the occurrence of two Hamiltonian flip bifurcations with respect to the other…
Mohammed O. AL-Kaff, Hamdy A. El-Metwally, El-Metwally M. Elabbasy
In this study, we investigate the dynamics of a discrete-time with predator-prey system with a Holling-III type functional response model. The center manifold theorem and bifurcation theory are used to create existence conditions for flip bifurcations and Neimark-Sacker bifurcations. Bifurcation diagrams, maximum…
Aqeel Ahmad, Fakher Abbas, Muhammad Farman, Evren Hincal + 3 more
'Abdul Ghaffar' 'Ali Akgül' 'Murad Khan Hassani'] To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by…
Yujiang Chen, Lin Li, Lingling Liu, Zhiheng Yu
In this paper, we delve into the dynamical properties of a class of threedimensional logistic ecological models. By using the complete discriminant theory of polynomials, we first give a topological classification for each fixed point and investigate the stability of corresponding system near the fixed points. Then…
Archishman Raju, Eric D. Siggia
The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington’s landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low…
Benjamin Apffel, Romain Fleury
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable state…
Soumyajit Seth, Abhijit Bera, Vikram Pakrashi
There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching…
Roberto Barrio, Santiago Ibáñez, Lucía Pérez
By studying a nonlinear model by inspecting a p-dimensional parameter space through $p-1$-dimensional cuts, one can detect changes that are only determined by the geometry of the manifolds that make up the bifurcation set. We refer to these changes as geometric bifurcations. They can be understood within the framework…
Maria Yampolskaya, Laertis Ikonomou, Pankaj Mehta
Multicellular organisms develop a wide variety of highly-specialized cell types. The consistency and robustness of developmental cell fate trajectories suggests that complex gene regulatory networks effectively act as low-dimensional cell fate landscapes. A complementary set of works draws on the theory of dynamical…
Ian Stewart
Shifts Authors: ['Ian Stewart'] Hopf bifurcation in networks of coupled ODEs creates periodic states in which the relative phases of nodes are well defined near bifurcation. When the network is a fully inhomogeneous nearest-neighbour coupled unidirectional ring, and node spaces are 1-dimensional, we derive constraints…
Mathieu Desroches, John Rinzel, Serafim Rodrigues, Hugues Berry
Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active…
Chi Zhai, Chunxi Yang, Jing Na, Xue-Bo Jin + 1 more
Information fusion integrates aspects of data and knowledge mostly on the basis that system information is accumulative/distributive, but a subtle case emerges for a system with bifurcations, which is always un-linearizable and exacerbates information acquisition and presents a control problem. In this paper, the…
Priscilla E. Greenwood, Lawrence M. Ward
Stochastic neural oscillations may be quasi-cycles or stochastic limit cycles. Here we discuss how and when these arise in stochastic dynamical systems with Hopf bifurcations, and point to relevant mathematical results. We describe a new type of oscillation, quasi-limit-cycles, which are limit cycles stirred up by…
Hanxuan Zhou
In this paper, by using eleven entangled quantum states as a quantum channel, we propose a cyclic and asymmetric novel protocol for four participants in which both Alice and Bob can transmit two-qubit states, and Charlie can transmit three-qubit states with the assistance of the supervisor David, who provides a…
Marisa Saggio
High-codimension bifurcations play a key role in shaping the dynamics of nonlinear models, as their unfoldings establish structured relationships between lower-codimension bifurcations and, ultimately, the attractors they generate. Owing to this unifying and predictive capacity, such bifurcations are attracting growing…
Marta del Olmo, Christoph Schmal, Camillo Mizaikoff, Saskia Grabe + 3 more
Three parameters are important to characterize a circadian and in general any biological clock: period, phase and amplitude. While circadian periods have been shown to correlate with entrainment phases, and clock amplitude influences the phase response of an oscillator to pulse-like zeitgeber signals, the…
Authors not listed
We present a chemical framework in which adaptive organization is achieved by tuning a gated quantum resonator (adaptive genomic resonator) {driven quantum oscillator} across a driven, dissipative reaction manifold (fitness landscape) {Hamiltonian potential surface}. In this view, catalytic elements set gain and phase…
Ayalur Raghu Subbalakshmi, Tamara Mirzapoiazova, Prakash Kulkarni, Ravi Salgia
In biology, oscillations are observed across a wide spectrum of processes and systems. Oscillatory systems are typically leveraged to transmit information within cells. However, they can also serve to transmit information between organisms underscoring their fundamental role in regulating transitions, maintaining…