Smallest Chimeras Under Repulsive Interactions

We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the repulsive interactions can only establish a symmetry of complete synchrony in the ring, which is broken with increasing repulsive interactions when the junctions pass through serials of asynchronous states (periodic and chaotic) but finally emerge into chimera states. The chimera pattern first appears in chaotic rotational motion of the three junctions when two junctions evolve coherently, while the third junction is incoherent. For larger repulsive coupling, the junctions evolve into another chimera pattern in a periodic state when two junctions remain coherent in rotational motion and one junction transits to incoherent librational motion. This chimera pattern is sensitive to initial conditions in the sense that the chimera state flips to another pattern when two junctions switch to coherent librational motion and the third junction remains in rotational motion, but incoherent. The chimera patterns are detected by using partial and global error functions of the junctions, while the librational and rotational motions are identified by a libration index. All the collective states, complete synchrony, desynchronization, and two chimera patterns are delineated in a parameter plane of the ring of junctions, where the boundaries of complete synchrony are demarcated by using the master stability function.

Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays

This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of an almost periodic state of the model are investigated and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. In addition, sufficient conditions for the global Mittag–Leffler stability of the almost periodic solutions are proposed. To justify our findings a numerical example is also presented.

Impact of COVID-19 Lockdown on Sleep Quality in Students

A periodic state of rest accompanied by varying degrees of unconsciousness and relative inactivity is referred as sleep; in another way is a state in which an individual lacks conscious awareness of environment surroundings. Quality sleep and getting enough of it at the right times is as essential for survival just as food and water. Without sleep our brain can’t learn and create new memories, making it harder to concentrate and respond quickly. The Novel Coronavirus (also known as COVID-19) ushered the world into uncharted waters. In India, strict lockdown was imposed in three phases from March to June 2020 for the containment of the COVID-19 pandemic. At this juncture, we attempted to assess how derailment of social life due to imposed social isolation, leading to compromised sleep in the present scenario affects circadian driven sleep-wake pattern and other lifestyle related behaviour. A brief survey on affected sleep pattern of people during corona pandemic was conducted to understand the possible alterations in sleep-wake schedules and the daily routine related activities such as exposure time to digital media (i.e., TV, laptop/computer/mobile, etc.) as a consequence of lockdown.

Dynamic Behavior Analysis of an Axially Loaded Beam Supported by a Nonlinear Spring-Mass System

Dynamic analysis of an Euler–Bernoulli beam with nonlinear supports is receiving greater research interest in recent years. Current studies usually consider the boundary and internal nonlinear supports separately, and the system rotational restraint is usually ignored. However, there is little study considering the simultaneous existence of axial load, lumped mass and internal supports for such nonlinear problem. Motivated by this limitation, the dynamic behavior of an axially loaded beam supported by a nonlinear spring-mass system is solved and investigated in this paper. Modal functions of an axially loaded Euler–Bernoulli beam with linear elastic supports are taken as trail functions in Galerkin discretization of the nonlinear governing differential equation. Stable steady-state response of such axially loaded beam supported by a nonlinear spring-mass system is solved via Galerkin truncation method, which is also validated by finite difference method. Results show that parameters of nonlinear spring-mass system and boundary condition have a significant influence on system dynamic behavior. Moreover, appropriate nonlinear parameters can switch the system behavior between the single-periodic state and quasi-periodic state effectively.

Dynamic behavior of fractional-order memristive time-delay system and image encryption application

This paper presents dynamic behavior of a fractional-order memristive time-delay system and its application in image encryption. First, a fractional-order memristive time-delay system is proposed, and the stability and bifurcation behaviors of the system are theoretically analyzed. Some limited conditions for describing the stability interval and switching between different dynamic behaviors are derived. Second, the dynamic characteristics of the system are analyzed through the coexisting attractors, coexisting bifurcation diagrams, the Largest Lyapunov exponents (LLE), the 0-1 test. When parameters change, such as time delay and fractional order, the system transits from steady state to periodic state, single scroll chaotic state, double scroll chaotic state. Furthermore, an image encryption scheme based on the fractional-order memristive time-delay system is introduced, and some statistical features are analyzed. Finally, numerical simulations verify the validity of the theoretical analysis and safety of the image encryption scheme based on the fractional-order delayed memristive chaotic system.

On the Spectral Properties for the Linearized Problem around Space-Time-Periodic States of the Compressible Navier–Stokes Equations

This paper studies the linearized problem for the compressible Navier-Stokes equation around space-time periodic state in an infinite layer of Rn (n=2,3), and the spectral properties of the linearized evolution operator is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the asymptotic expansions of the Floquet exponents near the imaginary axis for the Bloch transformed linearized problem are obtained for small Bloch parameters, which would give the asymptotic leading part of the linearized solution operator as t→∞.

Nonlinear dynamic characteristics of marine rotor-bearing system under coupled heave and pitch ship motions

The coupled heave and pitch motions of a ship sailing in head waves affect the stability of the marine rotor-bearing system. Based on the theory of analytical mechanics, this study establishes a dynamic model of the rotor-bearing system subjected to the coupled motions of heave and pitch, considering nonlinear oil film moments produced by the tilting of the rotor in the bearings. The nonlinear dynamic behaviours of the system are analysed using numerical methods to obtain Poincaré sections, bifurcation diagrams, and the largest Lyapunov exponents. The results show that dynamic bifurcation characteristics reveal complex quasi-periodic motion of upper and lower branches after the initial instability of the system, and the speed of second instability increase markedly. At high speeds, the amplitude of the rotor system increases sharply, which can cause the rotor to touch the inner wall of the bearings in the quasi-periodic state and a failure to transition to the chaotic state. Additionally, the effects of heave and pitch amplitude variations on the dynamic characteristics of the system are also discussed.

Infinite-dimensional Lur’e systems with almost periodic forcing

We consider forced Lur’e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay and partial differential equations are known to belong to this class of infinite-dimensional systems. We present refinements of recent incremental input-to-state stability results (Guiver in SIAM J Control Optim 57:334–365, 2019) and use them to derive convergence results for trajectories generated by Stepanov almost periodic inputs. In particular, we show that the incremental stability conditions guarantee that for every Stepanov almost periodic input there exists a unique pair of state and output signals which are almost periodic and Stepanov almost periodic, respectively. The almost periods of the state and output signals are shown to be closely related to the almost periods of the input, and a natural module containment result is established. All state and output signals generated by the same Stepanov almost periodic input approach the almost periodic state and the Stepanov almost periodic output in a suitable sense, respectively, as time goes to infinity. The sufficient conditions guaranteeing incremental input-to-state stability and the existence of almost periodic state and Stepanov almost periodic output signals are reminiscent of the conditions featuring in well-known absolute stability criteria such as the complex Aizerman conjecture and the circle criterion.

Effects of Yoga on Sleep Quality, Depression, Anxiety, Stress, and Blood Glucose Levels Among Tertiary Students

Sleep is defined as an easily reversible periodic state marked by the absence of wakefulness. Studies have shown that university students tend to have a diminished amount of sleep. This would lead to the loss of concentration, daytime sleepiness, and reduced academic performances. The aim of this study was to investigate the effects of yoga on overall sleep quality, depression, anxiety, stress, and blood glucose levels. A total of 88 participants with 44 students in each group, control and experimental, were recruited from Universiti Tunku Abdul Rahman based on the outcome of the Godin Shephard questionnaire. A total score of less than 14 was considered mild hence falling into the control group while above 14 and had practiced yoga for a minimum of 6 weeks were placed in the experimental group. The participants were required to self-administer a set of questionnaires consisting of socio-demographic information, the Pittsburgh Sleep Quality Index (PSQI) questionnaire and Depression, Anxiety, Stress Scores. Three components of sleep, namely the habitual sleep efficiency, sleep disturbances, and daytime dysfunctions, were better in the experimental group compared to the control one. Depression, anxiety, stress, and blood glucose levels also appeared to be more desirable in the experimental group with yoga students. It was found that blood glucose levels were positively correlated to the Global PSQI score, depression, anxiety, and stress measures in this study. In conclusion, yoga-practicing students have healthier sleep patterns, negative emotional states, and blood glucose levels. In order to obtain more conclusive findings, similar studies should be carried out in different universities with larger sample size and for longer periods.

Induction of chaotic fluctuations in particle dynamics in a uniformly accelerated frame

The ongoing conjecture that the presence of horizon may induce chaos in an integrable system, is further investigated from the perspective of a uniformly accelerated frame. Particularly, we build up a model which consists of a particle (massless and chargeless) trapped in harmonic oscillator in a uniformly accelerated frame (namely Rindler observer). Here, the Rindler frame provides a Killing horizon without any intrinsic curvature to the system. This makes the present observations different from previous studies. We observe that for some particular values of parameters of the system (like acceleration, energy of the particle), the motion of the particle trapped in harmonic potential systematically goes from periodic state to the chaotic. This indicates that the existence of horizon alone, not the intrinsic curvature (i.e. the gravitational effect) in the background, is sufficient to induce the chaotic motion in the particle. We believe the present study further enlighten and balustrade the conjecture.