21 papers · ranked by Valyu relevance
Krishna Manoj, Samadhan A. Pawar, R. I. Sujith
Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon…
T. M. Bury, C. T. Bauch, M. Anand
Theory and observation tell us that many complex systems exhibit tipping points-thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical…
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…
Krishna Pusuluri, Hil G. E. Meijer, Andrey Shilnikov
We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using…
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…
Andrus Giraldo, Bernd Krauskopf, Hinke M. Osinga
When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes on itself in an orientable or non-orientable way, provided the corresponding genericity conditions. We are interested in the interaction…
Mochamad Apri, Jaap Molenaar, Maarten de Gee, George van Voorn + 1 more
'Diego Di Bernardo'] Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the Laub-Loomis model, a nonlinear model for…
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…
Claire Postlethwaite, A. M. Rucklidge
One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories…
J. J. Williamson, P. D. Olmsted
Compositional asymmetry between the leaflets of bilayer membranes is known to couple strongly to their phase behaviour, in addition to having important effects on, e.g., mechanical properties and protein activity. We address how phase behaviour is affected by passive phospholipid flip-flop, such that the compositional…
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…
Marek Berezowski, Artur Grabski
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the solutions of the mathematical method are characterized by no dynamic bifurcations. It…
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…
Humberto Arce, Araceli Torres, Augusto Cabrera, Martín Alarcón + 1 more
'Carlos Málaga'] The Tantalus Oscillator is a non linear hydrodynamic oscillator with an attractive limit cycle. In this study we pursue the construction of a biparametric bifurcation diagram for the Tantalus Oscillator under biphasics perturbations. That is the first time that this kind of diagram is built for this…
Lucia Russo, Konstantinos Spiliotis, Francesco Giannino, Stefano Mazzoleni + 1 more
'Stefano Mazzoleni' 'Constantinos Siettos'] Ecosystems may be characterized by a complex dynamical behaviour where external disturbances and/or internal perturbations may trigger sudden/irreversible changes, called catastrophic shifts. Simple mathematical models in the form of ordinary and/or partial differential…
Elisabeth Roesch, Michael P.H. Stumpf
Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in…
Evgeni V. Nikolaev, Sahand Jamal Rahi, Eduardo D. Sontag
This paper uncovers a remarkable behavior in two biochemical systems that commonly appear as components of signal transduction pathways in systems biology. These systems have globally attracting steady states when unforced, so they might have been considered “uninteresting” from a dynamical standpoint. However, when…
D. Battogtokh, J. J. Tyson
Mathematical models of fundamental biological processes play an important role in consolidating theory and experiments, especially if they are systematically developed, thoroughly characterized, and well tested by experimental data. In this work, we report a detailed bifurcation analysis of a mathematical model of the…
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…
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…