Emergence of Stripe-Core Mixed Spiral Chimera on a Spherical Surface of Nonlocally Coupled Oscillators

2021 ◽  
Vol 31 (12) ◽  
pp. 2150182
Author(s):  
Ryong-Son Kim ◽  
Gi-Hun Tae ◽  
Chol-Ung Choe
Keyword(s):  
Coupled Oscillators ◽  
Spherical Surface ◽  
Spiral Wave ◽  
Stability Diagram ◽  
Phase Oscillators ◽  
Type Region ◽  
Chimera State ◽  
Existence And Stability ◽  
The Stability ◽  
Theoretical Results

We report on a stripe-core mixed spiral chimera in a system of nonlocally coupled phase oscillators, located on the spherical surface, where the spiral wave consisting of phase-locked oscillators is separated by a stripe-type region of incoherent oscillators into two parts. We analyze the existence and stability of the stripe-core mixed spiral chimera state rigorously, on the basis of the Ott–Antonsen reduction theory. The stability diagram for the stationary states including the spiral chimeras as well as incoherent state is presented. Our stability analysis reveals that the stripe-core mixed spiral chimera state emerges as a unique attractor and loses its stability via the Hopf bifurcation. We verify our theoretical results using direct numerical simulations of the model system.

scholarly journals Cascades of Multiheaded Chimera States for Coupled Phase Oscillators

2014 ◽  
Vol 24 (08) ◽  
pp. 1440014 ◽  
Author(s):  
Yuri L. Maistrenko ◽  
Anna Vasylenko ◽  
Oleksandr Sudakov ◽  
Roman Levchenko ◽  
Volodymyr L. Maistrenko
Keyword(s):  
Periodic Orbit ◽  
Coupled Oscillators ◽  
Phase Oscillators ◽  
Invariant Circle ◽  
Saddle Node Bifurcation ◽  
Chimera States ◽  
Chimera State ◽  
Self Organized ◽  
Saddle Node ◽  
Different Types

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.

scholarly journals CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS

2006 ◽  
Vol 16 (01) ◽  
pp. 21-37 ◽  
Author(s):  
DANIEL M. ABRAMS ◽  
STEVEN H. STROGATZ
Keyword(s):  
Traveling Waves ◽  
Collective Behavior ◽  
Coupled Oscillators ◽  
Spatiotemporal Chaos ◽  
Phase Oscillators ◽  
Nonlocal Coupling ◽  
One Dimensional ◽  
Chimera State ◽  
Global Coupling ◽  
Pattern Forming

Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-forming systems, such as neural networks, convecting fluids, laser arrays and coupled biochemical oscillators. These systems are known to exhibit rich collective behavior, from synchrony and traveling waves to spatiotemporal chaos and incoherence. Recently, Kuramoto and his colleagues reported a strange new mode of organization — here called the chimera state — in which coherence and incoherence exist side by side in the same system of oscillators. Such states have never been seen in systems with either local or global coupling; they are apparently peculiar to the intermediate case of nonlocal coupling. Here we give an exact solution for the chimera state, for a one-dimensional ring of phase oscillators coupled nonlocally by a cosine kernel. The analysis reveals that the chimera is born in a continuous bifurcation from a spatially modulated drift state, and dies in a saddle-node collision with an unstable version of itself.

Dynamical analysis of a two-species competitive system with state feedback impulsive control

2020 ◽  
Vol 13 (05) ◽  
pp. 2050007
Author(s):  
Jing Xu ◽  
Mingzhan Huang ◽  
Xinyu Song
Keyword(s):  
Periodic Solution ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Competitive System ◽  
Competitive Systems ◽  
State Dependent ◽  
Existence And Stability ◽  
The Stability ◽  
Theoretical Results

In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

CHARGE STABILITY AND CONDUCTANCE ANALYSIS OF ANTHRACENE-BASED SINGLE ELECTRON TRANSISTOR

2013 ◽  
Vol 12 (06) ◽  
pp. 1350045 ◽  
Author(s):  
ANURAG SRIVASTAVA ◽  
BODDEPALLI SANTHIBHUSHAN ◽  
PANKAJ DOBWAL
Keyword(s):  
Coulomb Blockade ◽  
Density Functional ◽  
Stability Diagram ◽  
Single Electron ◽  
Single Electron Transistor ◽  
Functional Theory ◽  
Charge Stability ◽  
Anthracene Molecule ◽  
The Stability ◽  
Experimental Values

The present paper discusses the investigation of electronic properties of anthracene-based single electron transistor (SET) operating in coulomb blockade region using Density Functional Theory (DFT) based Atomistix toolkit-Virtual nanolab. The charging energies of anthracene molecule in isolated as well as electrostatic SET environments have been calculated for analyzing the stability of the molecule for different charge states. Study also includes the analysis of SET conductance dependence on source/drain and gate potentials in reference to the charge stability diagram. Our computed charging energies for anthracene in isolated environment are in good agreement with the experimental values and the proposed anthracene SET shows good switching properties in comparison to other acene series SETs.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

Sign in / Sign up

Export Citation Format

Share Document