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Bishwajit Paul, Tanmoy Banerjee
Digital phase-locked loops (DPLLs) are nonlinear feedback-controlled systems that are widely used in electronic communication and signal processing applications. In most of the applications, they work in coupled mode; however, a vast amount of the studies on DPLLs concentrate on the dynamics of a single isolated unit. In this paper, we consider both one- and two-dimensional networks of DPLLs connected through a practically realistic nonlocal coupling and explore their collective dynamics. For the one-dimensional network, we analytically derive the parametric zone of a stable phase-locked state in which DPLLs essentially work in their normal mode of operation...
January 2019: Chaos
Jakub Spiechowicz, Jerzy Łuczka
We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime of the noise induced dynamical localization of the Josephson phase velocity, i.e., there is a temperature interval in which the conditional probability of the voltage to remain in one of the states is very close to one...
January 2019: Chaos
Jürgen Kurths
No abstract text is available yet for this article.
January 2019: Chaos
Prosenjit Kundu, Lekha Sharma, Mauparna Nandan, Dibakar Ghosh, Chittaranjan Hens, Pinaki Pal
We investigate different emergent dynamics, namely, oscillation quenching and revival of oscillation, in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory state (OS), we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states from the homogeneous steady state sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state, i...
January 2019: Chaos
Kolade M Owolabi
In this paper, we analyze the stability of the equilibrium point and Hopf bifurcation point in the three-component time-fractional differential equation, which describes the predator-prey interaction between different species. In the dynamics, the classical first-order derivative in time is modelled by either the Caputo or the Atangana-Baleanu fractional derivative of order α,0<α<1. We utilized a fractional version of the Adams-Bashforth formula to discretize these fractional derivatives in time. The results of the linear stability analysis presented are confirmed by computer simulation results...
January 2019: Chaos
Konstantin Fackeldey, Péter Koltai, Peter Névir, Henning Rust, Axel Schild, Marcus Weber
Given a time-dependent stochastic process with trajectories x(t) in a space Ω, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable setsM are defined in space M⊂Ω, and coherent setsM(t)⊂Ω are defined in space and time. Hence, if we extend the space Ω by the time-variable t, coherent sets are metastable sets in Ω×[0,∞) of an appropriate space-time process. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets...
January 2019: Chaos
Yanfei Du, Ben Niu, Junjie Wei
In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation and double Hopf bifurcation are investigated on the parametric plane of two delays. Taking two time delays as bifurcation parameters, the normal form on the center manifold near the double Hopf bifurcation point is derived, and the unfoldings near the critical points are given...
January 2019: Chaos
Michael Rosenblum, Arkady Pikovsky
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms...
January 2019: Chaos
Mohammed Al-Refai, Mohamed Ali Hajji
In this paper, we study linear and nonlinear fractional eigenvalue problems involving the Atangana-Baleanu fractional derivative of the order 1<δ<2. We first estimate the fractional derivative of a function at its extreme points and apply it to obtain a maximum principle for the linear fractional boundary value problem. We then estimate the eigenvalues of the nonlinear eigenvalue problem and obtain necessary conditions to guarantee the existence of eigenfunctions. We also obtain a uniqueness result and a norm estimate of solutions of the linear problem...
January 2019: Chaos
Nazmi Burak Budanur, Marc Fleury
We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application of dynamical systems theory tools. As an illustration of the utility of the symmetry reduction, we apply it to a model of the pilot-wave system with a central harmonic force. We begin our analysis by identifying local bifurcations and the onset of chaos. We then describe the emergence of chaotic regions and their merging bifurcations, which lead to the formation of a global attractor...
January 2019: Chaos
Prosenjit Kundu, Pinaki Pal
We investigate transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage (f) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution, namely, Lorentz distribution. The effects of variation of f and phase frustration parameter α on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength (λc ) and group angular velocity (Ωc ) at the onset of synchronization have been derived analytically in the thermodynamic limit...
January 2019: Chaos
Sania Qureshi, Abdullahi Yusuf, Asif Ali Shaikh, Mustafa Inc, Dumitru Baleanu
In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained...
January 2019: Chaos
Hayder Natiq, Santo Banerjee, M R K Ariffin, M R M Said
In this paper, we investigate the dynamical behavior in an M-dimensional nonlinear hyperchaotic model (M-NHM), where the occurrence of multistability can be observed. Four types of coexisting attractors including single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors can be found, which are unusual behaviors in discrete chaotic systems. Furthermore, the coexistence of asymmetric and symmetric properties can be distinguished for a given set of parameters...
January 2019: Chaos
Sajjad Ali Khan, Kamal Shah, Gul Zaman, Fahd Jarad
In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab...
January 2019: Chaos
Yuan Cao, Yuzhuo Zhang, Tao Wen, Peng Li
In order to control the nonlinear high-speed train with high robustness, the fractional order control of nonlinear switching systems is studied. The fractional order controller is designed for a class of nonlinear switching systems by the fractional order backstepping method. In this paper, a simple and effective online updating scheme of model coefficients is proposed by using the flexibility of the model predictive control algorithm and its wide range of model accommodation. A stochastic discrete nonlinear state space model describing the mechanical behavior of a single particle in a high-speed train is constructed, and the maximum likelihood estimation of the parameters of a high-speed train is transformed into an optimization problem with great expectations...
January 2019: Chaos
Kolade M Owolabi, Zakia Hammouch
The aim of this paper is to apply the newly trending Atangana-Baluanu derivative operator to model some symbiosis systems describing commmensalism and predator-prey processes. The choice of using this derivative is due to the fact that it combines nonlocal and nonsingular properties in its formulation, which are the essential ingredients when dealing with models of real-life applications. In addition, it is only the Atangana-Baleanu derivative that has both Markovian and non-Markovian properties. Also, its waiting time takes into account the power, exponential, and Mittag-Leffler laws in its formulation...
January 2019: Chaos
M M El-Dessoky, M A Khan
This paper presents the analysis of fractional order dynamical system of combined modified function projective synchronization of different systems. Initially, we formulate the model in fractional order and then investigate their associated properties. We then investigate the chaotic behavior of different systems by considering the fractional order parameter. To obtain the simulation results of the models, we use the Runge-Kutta order four scheme and Adams-Bashforth scheme. The obtained results are discussed in detail for the various values of the fractional order parameters...
January 2019: Chaos
Shaofei Wu
The use of mathematical methods has become an indispensable research tool and method in the establishment and improvement of many disciplines. Therefore, mathematical methods have also been included in the intelligence analysis system of public security information science. Intelligence is a summary of information that exists in all aspects of our lives. This information is distributed according to time based on certain rules. The application of mathematical analysis methods can more accurately extract effective information and predict future trends...
January 2019: Chaos
Fengrong Zhang, Deliang Qian, Changpin Li
In this paper, we study finite-time stability of fractional differential systems with variable coefficients, which includes the homogeneous and nonhomogeneous delayed cases. Based on the theories of fractional differential equations, we obtain three theorems on the finite-time stability, which give some sufficient conditions on finite-time stability, respectively, for homogeneous systems without and with time delay and for the nonhomogeneous system with time delay.
January 2019: Chaos
P Veeresha, D G Prakasha, Haci Mehmet Baskonus
In this paper, we apply the q-homotopy analysis transform method to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional. We find some new approximate numerical results for different values of parameters of alpha. Then, we present novel simulations for all cases of results conducted by considering the values of parameters of alpha in terms of two- and three-dimensional figures along with tables including critical numerical values.
January 2019: Chaos
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