Emergent behaviors of the swarmalator model for position-phase aggregation

2019 ◽  
Vol 29 (12) ◽  
pp. 2225-2269 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Jinwook Jung ◽  
Jeongho Kim ◽  
Jinyeong Park ◽  
Xiongtao Zhang
Keyword(s):  
Upper Bound ◽  
Phase Synchronization ◽  
Sufficient Conditions ◽  
Particle Systems ◽  
Particle Aggregation ◽  
Type Model ◽  
Collective Behaviors ◽  
Emergent Behaviors ◽  
Dynamic Interplay ◽  
Phase Differences

We study emergent dynamics of the swarmalator model [K. P. O’Keeffe, H. Hong and S. H. Strogatz, Oscillators that sync and swarm, Nature Commun. 8 (2017) 1504] describing the dynamic interplay of aggregation and synchronization dynamics for interacting many-particle systems. For the particle aggregation, we employ the nonlinear aggregation system with singular attractive–repulsive couplings depending on the phase differences, while we use the Kuramoto-type model with the singular coupling strength depending on the spatial distances for the dynamics of phases. We show how collective behaviors emerge from the dynamic interplay between position aggregation and phase synchronization. We introduce some sufficient framework leading to the positive minimal relative distances between particles and its uniform upper bound. We also show the convergence of position under some sufficient conditions.

scholarly journals Collision-avoidance and flocking in the Cucker–Smale-type model with a discontinuous controller

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jianfei Cheng ◽  
Xiao Wang ◽  
Yicheng Liu
Keyword(s):  
Weight Function ◽  
Collision Avoidance ◽  
Upper Bound ◽  
Finite Time ◽  
Relative Velocity ◽  
Sufficient Conditions ◽  
Repulsive Force ◽  
Type Model ◽  
Movement Tendency ◽  
Special Case

<p style='text-indent:20px;'>The collision-avoidance and flocking of the Cucker–Smale-type model with a discontinuous controller are studied. The controller considered in this paper provides a force between agents that switches between the attractive force and the repulsive force according to the movement tendency between agents. The results of collision-avoidance are closely related to the weight function <inline-formula><tex-math id="M1">\begin{document}$ f(r) = (r-d_0)^{-\theta } $\end{document}</tex-math></inline-formula>. For <inline-formula><tex-math id="M2">\begin{document}$ \theta \ge 1 $\end{document}</tex-math></inline-formula>, collision will not appear in the system if agents' initial positions are different. For the case <inline-formula><tex-math id="M3">\begin{document}$ \theta \in [0,1) $\end{document}</tex-math></inline-formula> that not considered in previous work, the limits of initial configurations to guarantee collision-avoidance are given. Moreover, on the basis of collision-avoidance, we point out the impacts of <inline-formula><tex-math id="M4">\begin{document}$ \psi (r) = (1+r^2)^{-\beta } $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ f(r) $\end{document}</tex-math></inline-formula> on the flocking behaviour and give the decay rate of relative velocity. We also estimate the lower and upper bound of distance between agents. Finally, for the special case that agents moving on the 1-D space, we give sufficient conditions for the finite-time flocking.</p>

scholarly journals Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chun-xia Dou ◽  
Zhi-sheng Duan ◽  
Xing-bei Jia ◽  
Xiao-gang Li ◽  
Jin-zhao Yang ◽  
...  
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Upper Bound ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Large System ◽  
Disturbance Attenuation ◽  
Robust Controller ◽  
Large Systems ◽  
Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

scholarly journals A strict upper bound for size multipartite Ramsey numbers of paths versus stars

2017 ◽  
Vol 1 (2) ◽  
pp. 9
Author(s):  
Chula Jayawardene
Keyword(s):  
Natural Number ◽  
Complete Graph ◽  
Upper Bound ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Infinite Class ◽  
Ramsey Numbers ◽  
Necessary And Sufficient

<p>Let $P_n$ represent the path of size $n$. Let $K_{1,m-1}$ represent a star of size $m$ and be denoted by $S_{m}$. Given a two coloring of the edges of a complete graph $K_{j \times s}$ we say that $K_{j \times s}\rightarrow (P_n,S_{m+1})$ if there is a copy of $P_n$ in the first color or a copy of $S_{m+1}$ in the second color. The size Ramsey multipartite number $m_j(P_n, S_{m+1})$ is the smallest natural number $s$ such that $K_{j \times s}\rightarrow (P_n,S_{m+1})$. Given $j,n,m$ if $s=\left\lceil \dfrac{n+m-1-k}{j-1} \right\rceil$, in this paper, we show that the size Ramsey numbers $m_j(P_n,S_{m+1})$ is bounded above by $s$ for $k=\left\lceil \dfrac{n-1}{j} \right\rceil$. Given $j\ge 3$ and $s$, we will obtain an infinite class $(n,m)$ that achieves this upper bound $s$. In the later part of the paper, will also investigate necessary and sufficient conditions needed for the upper bound to hold.</p>

scholarly journals Existence and uniqueness of analytic solutions of the Shabat equation

2005 ◽  
Vol 2005 (8) ◽  
pp. 855-862 ◽  
Author(s):  
Eugenia N. Petropoulou
Keyword(s):  
Upper Bound ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Analytic Solution ◽  
Sufficient Conditions ◽  
Analytic Solutions ◽  
Initial Condition ◽  
Initial Value ◽  
First Derivative

Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely forz∈ℂ:|z|<T,T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, andT. Furthermore, from these conditions, one can obtain an upper bound forT. Our results are in consistence with some recently found results.

Delay-dependent stability analysis for discrete-time switched linear systems with parametric uncertainties

2017 ◽  
Vol 24 (20) ◽  
pp. 4921-4930 ◽  
Author(s):  
Nasrollah Azam Baleghi ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Discrete Time ◽  
Upper Bound ◽  
Sufficient Conditions ◽  
Switched System ◽  
Parametric Uncertainties ◽  
Time Varying ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper studies the delay-dependent stability conditions for time-delay discrete-time switched systems. In the considered switched system, there are uncertain terms in each subsystem due to affine parametric uncertainties. Additionally, each subsystem has a time-varying state delay which adds more complexity to the stability analysis. Based on the Lyapunov functional approach, the sufficient conditions are extracted to determine the admissible upper bound of the time-varying delay for guaranteed stability. Furthermore, a class of switching signals is identified to guarantee the exponential stability of the uncertain time-delay switched system. The main advantage of the suggested switching signals is its independency to the uncertainties. Furthermore, these signals are only constrained by a determined average dwell time (may be chosen arbitrarily). Finally, a numerical example is provided to demonstrate the efficiency of the proposed method and also the reduction of conservatism in finding the admissible upper bound of time-delay in comparison with other stability analysis approaches.

Local conditions for the stochastic comparison of particle systems

2004 ◽  
Vol 36 (4) ◽  
pp. 1252-1277 ◽  
Author(s):  
Rosario Delgado ◽  
F. Javier López ◽  
Gerardo Sanz
Keyword(s):  
Queueing Networks ◽  
Interacting Particle Systems ◽  
Sufficient Conditions ◽  
Explicit Construction ◽  
Particle Systems ◽  
Stochastic Comparison ◽  
Local Conditions ◽  
Jackson Networks ◽  
Finite Set ◽  
Necessary And Sufficient

We study the stochastic comparison of interacting particle systems where the state space of each particle is a finite set endowed with a partial order, and several particles may change their value at a time. For these processes we give local conditions, on the rates of change, that assure their comparability. We also analyze the case where one of the processes does not have any changes that involve several particles, and obtain necessary and sufficient conditions for their comparability. The proofs are based on the explicit construction of an order-preserving Markovian coupling. We show the applicability of our results by studying the stochastic comparison of infinite-station Jackson networks and batch-arrival, batch-service, and assemble-transfer queueing networks.

APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350055 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHANG-YUAN CHENG ◽  
YI-RU LIN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Type Model ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Trapping Region ◽  
Saddle Node ◽  
The Stability ◽  
Two Equilibria

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh–Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov–Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov–Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations.

scholarly journals Investigating climate tipping points under various emission reduction and carbon capture scenarios with a stochastic climate model

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Alexander Mendez ◽  
Mohammad Farazmand
Keyword(s):  
Upper Bound ◽  
Emission Reduction ◽  
Carbon Capture ◽  
Climate Model ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Tipping Point ◽  
Balance Model ◽  
Critical Threshold ◽  
Stochastic Climate Model

We study the mitigation of climate tipping point transitions using an energy balance model. The evolution of the global mean surface temperature is coupled with the CO 2 concentration through the green-house effect. We model the CO 2 concentration with a stochastic delay differential equation (SDDE), accounting for various carbon emission and capture scenarios. The resulting coupled system of SDDEs exhibits a tipping point phenomena: if CO 2 concentration exceeds a critical threshold (around 478   ppm ), the temperature experiences an abrupt increase of about six degrees Celsius. We show that the CO 2 concentration exhibits a transient growth which may cause a climate tipping point, even if the concentration decays asymptotically. We derive a rigorous upper bound for the CO 2 evolution which quantifies its transient and asymptotic growths, and provides sufficient conditions for evading the climate tipping point. Combining this upper bound with Monte Carlo simulations of the stochastic climate model, we investigate the emission reduction and carbon capture scenarios that would avert the tipping point.

scholarly journals Emergent myxobacterial behaviors arise from reversal suppression induced by kin contacts

2021 ◽  
Author(s):  
Rajesh Balagam ◽  
Pengbo Cao ◽  
Govind P Sah ◽  
Zhaoyang A Zhang ◽  
Daniel Wall ◽  
...  
Keyword(s):  
Kin Recognition ◽  
Social Recognition ◽  
Collective Behaviors ◽  
Large Numbers ◽  
Wide Range ◽  
Chemosensory Pathway ◽  
Cellular Slime ◽  
Physical Interactions ◽  
Mechanistic Basis ◽  
Emergent Behaviors

A wide range of biological systems - from microbial swarms to bird flocks, display emergent behaviors driven by coordinated movement of individuals. To this end, individual organisms interact by recognizing their kin and adjusting their motility based on others around them. However, even in the best-studied systems, the mechanistic basis of the interplay between kin recognition and motility coordination is not understood. Here, using a combination of experiments and mathematical modeling, we uncover the mechanism of an emergent social behavior in Myxococcus xanthus. By overexpressing the cell surface kin recognition receptors, TraA and TraB, large numbers of cells adhere to one another and form organized macroscopic circular aggregates that spin clockwise or counterclockwise. Mechanistically, TraAB adhesion results in sustained cell-cell contacts that signal the Frz chemosensory pathway. In turn, cell reversals are suppressed and circular aggregates form as the result of cells' ability to follow cellular slime trails. Furthermore, our in-silico simulations demonstrate a remarkable ability to predict self-organization patterns when phenotypically distinct strains are mixed. Therefore, this work provides key mechanistic insights into M. xanthus social interactions and demonstrates how social recognition transforms physical interactions into emergent collective behaviors.

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