The dynamics of a delayed generalized fractional-order biological networks with predation behavior and material cycle

In this paper, a delayed generalized fractional-order biological networks with predation behavior and material cycle is comprehensively discussed. Some criteria of stability and bifurcation for the present system is presented. Moreover some results of two delays are obtained. Finally, some numerical simulations are presented to support the analytical results

Synchronous dynamics of a delayed two-coupled oscillator

This paper presents a detailed analysis on the dynamics of a delayed two-coupled oscillator. Linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. By means of the equivariant Hopf bifurcation theorem, we not only investigate the effect of time delay on the spatio-temporal patterns of periodic solutions emanating from the trivial equilibrium, but also derive the formula to determine the direction and stability of Hopf bifurcation. Moreover, we illustrate our results by numerical simulations

Dynamic analysis and optimal control of a novel fractional-order 2I2SR rumor spreading model

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then the next-generation matrix method is used to calculate the threshold. Furthermore, the stability of rumor-free/spreading equilibrium is discussed based on fractional-order Routh–Hurwitz stability criterion, Lyapunov function method, and invariance principle. Next, the necessary conditions for fractional optimal control are obtained. Finally, some numerical simulations are given to verify the results

The Dynamics of Coupled Oscillators

The subject is introduced by considering the treatment of oscillators in Mathematics from the simple Poincar´e oscillator, a single variable dynamical process defined on a circle, to the oscillatory dynamics of systems of differential equations. Some models of real oscillator systems are considered. Noise processes are included in the dynamics of the system. Coupling between oscillators is investigated both in terms of analytical systems and as coupled oscillator models. It is seen that driven oscillators can be used as a model of 2 coupled oscillators in 2 and 3 dimensions due to the dependence of the dynamics on the phase difference of the oscillators. This means that the dynamics are easily able to be modelled by a 1D or 2D map. The analysis of N coupled oscillator systems is also described. The human cardiovascular system is studied as an example of a coupled oscillator system. The heart oscillator system is described by a system of delay differential equations and the dynamics characterised. The mechanics of the coupling with the respiration is described. In particular the model of the heart oscillator includes the baroreceptor reflex with time delay whereby the aortic fluid pressure influences the heart rate and the peripheral resistance. Respiration is modelled as forcing the heart oscillator system. Locking zones caused by respiratory sinus arrhythmia (RSA), the synchronisation of the heart with respiration, are found by plotting the rotation number against respiration frequency. These are seen to be relatively narrow for typical physiological parameters and only occur for low ratios of heart rate to respiration frequency. Plots of the diastolic pressure and heart interval in terms of respiration phase parameterised by respiration frequency illustrate the dynamics of synchronisation in the human cardiovascular system

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Exploiting nonlinearity and noise in optical tweezers and semiconductor lasers : from resonant damping to stochastic logic gates and extreme pulses

This thesis is focused on the study of stochastic and nonlinear dynamics in optical systems. First, we study experimentally the dynamics of a Brownian nanometer particle in an optical trap subjected to an external forcing. Specifically, we consider the effects of parametric noise added to a monostable or bistable optical trap and discovered a new effect which we named stochastic resonant damping (SRD). SRD concerns the minimization of the output variance position of a particle held in a harmonic trap, when an external parametric noise was added to the position trap. We compared the classical stochastic resonance (SR) with SRD and found that they are two phenomena which coexist in the same system but in different regimes. The experimentally studied monostable system showed a maximum in the signal to noise ratio, a clear signature of a resonance. We also developed a new technique to increase 10-fold the detection range of the quadrant photodiode that we used in this study, which exploits the channel crosstalk. Second, we study the stochastic dynamics of a type of semiconductor laser (SCL), known as vertical-cavity surface-emitting laser (VCSEL), that exhibits polarization bistability and hysteresis, either when the injection current or when the optically injected power are varied. We have shown how these properties can be exploited for logic operations due to the effect of the spontaneous emission noise. Two logical input signals have been encoded in three levels of optically injected power from a master laser, and the logical output response was decoded from the emitted polarization of the injected VCSEL. Correct and robust operation was obtained when the three levels of injected power were adjusted to favor one polarization at two levels and to favor the orthogonal polarization at the third level. We numerically demonstrated that the VCSEL-based logic operator allows to reproduce the truth table for the OR and NOR logic operators, while the extension to AND and NAND is straightforward. With this all-optical configuration we have been able to reduce the minimum bit time required for correct operation from 30 ns, obtained in a previous work with an optoelectronic configuration, to 5 ns. The third focus of this thesis is the study of the chaotic nonlinear dynamics of a SCL optically injected, in the regime where it can display sporadic huge intensities pulses, referred to as Rogue Waves (RWs). We found that, when adding optical noise, the region where RWs appear becomes wider. This behavior is observed for high enough noise; however, on the contrary, for very weak noise we found that noise diminishes the number of RW events in certain regions. In order to suppress or induce extreme pulses, we investigated the effects of an external periodic modulation of the laser current. We found that the modulation at specific frequencies modifies the dynamics from chaotic to periodic. Depending on the parameter region, current modulation can contribute to an increased threshold for RWs. Therefore, we concluded that the modulation can be effective for suppressing the RWs dynamics

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described