Vol. 12, No. 4 (2023): Regular Issue

In the present work, we present a new algorithm for assessing causality in uni-directionally weakly coupled chaotic oscillators embedded in heavy white Gaussian noise. This method is based on the correlation between changes in the phase dynamics of the slave oscillator and the dynamics of the phase difference between the oscillators. This can be applied when the phase difference is determined by the intrinsic frequencies of the oscillators, and the effect of the phase slip of the slave oscillator on the phase difference is nonsignificant. To recover the phase at a low signal-to-noise ratio (SNR), the wrapped phase is converted into sine and cosine formats and then denoised using a Fourier transformation followed by a recalculation of the wrapped phase values through those filtered terms. Application of the proposed approach to master-slave Rössler systems and coupled Stuart--Landau oscillators showed that the new algorithm is well-suited for assessing the presence and direction of coupling in highly noisy chaotic oscillators weakly coupled in a uni-directional manner. Specifically, directional coupling was reliably detected at a SNR of up to 0 dB for chaotic Rössler systems and for Stuart--Landau oscillators.

One of the major problems in classical mechanics is to determine the mean field potential in which the motion of a test particle takes place. In the light of the inverse problem of dynamics, we study three-dimensional genuine potentials $V=V(x,y,z)$ producing a set of two-parametric families of regular orbits $f(x,y,z)=c_{1}$, $g(x,y,z)=c_{2}$ ($c_{1}, \; c_{2}=$const.). We focus on homogeneous and axisymmetric potentials which have many physical applications. Then, we establish three differential conditions to be fulfilled by the given two-parametric families of orbits (traced in 3D space by a material point) so that these families can result in the presence of such a potential. All possible cases for the ``given'' family of orbits are studied and several compatible pairs of families and potentials are found. Finally, some potentials of physical interest are also presented.

Nowadays, a wireless sensor network (WSN) is an emerging and robust technology that can facilitate our everyday life. To investigate the assaulting conduct of worms in wireless sensor networks, we propose a Susceptible-Infected-Terminally-infected (SIT) model utilizing Holling type-II and Beddington-DeAngelis functional responses. The Positivity and boundedness of solutions of the model are analyzed to assure the feasibility of solutions. We determine the existence of possible equilibrium points under feasible conditions. With the aid of a characteristic equation, local stability analysis of all feasible equilibrium points is investigated. Global stability analysis of the steady states is also investigated under Lassalle's invariance principle and Bendixson-Dulac criteria. The global stability of the endemic equilibrium point is performed under a suitable Lyapunov function. Numerical simulations are performed to validate the analytical findings under suitable initial data. It is revealed that a Hopf bifurcation occurs where the endemic steady state of the system becomes unstable when the parameter $\omega_2$ is globally varied. Furthermore, a periodic time series and a period-doubling behavior are exposed in the system due to the instability of the endemic steady state in a parameter regime. Finally, the results are significantly beneficial to predict and control the spread of worms in a WSN.

In this paper, we consider a quaternion-valued cellular neural networks with time varying delays in leakage term on time scales. We derive sufficient conditions for the existence, uniqueness and global exponential stability of almost periodic solutions by using contraction mapping principle and exponential dichotomy of linear dynamic equations. Finally, a numerical example is provided to illustrate the feasibility of our results.

This paper investigates matrix and inverse matrix projective synchronization of chaotic and hyperchaotic systems with uncertainties and external disturbances. The sufficient conditions for achieving matrix projective synchronization (MPS) and inverse matrix projective synchronization (IMPS) of two chaotic and hyperchaotic systems are obtained. Two controllers, one for MPS and other for IMPS are designed for synchronization and based on the design, the synchronization of considered chaotic and hyperchaotic systems is achieved using these controllers. Lyapunov stability theory is used to study the problem and numerical simulations are introduced to exhibit the adequacy of the MPS and IMPS.

In this paper, we provide some sufficient conditions for the asymptotic stability of solutions of nonlinear dynamic systems with impulsive perturbations by using some inequality of Gronwall type. Practical exponential stability is also investigated for a class of perturbed impulsive systems. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results. Furthermore, Hopfield neural networks system is discussed as an application.

In this work, a discrete-time evolutionary Beverton-Holt population model is formulated. The existence and local asymptotic stability of the positive equilibrium point are studied. It is also shown that the discrete model can undergo a Neimark-Sacker bifurcation (NSB) in a small neighborhood of the positive equilibrium under certain conditions. In order to control chaos, we employ the Ott-Grebogi-Yorke (OGY) method and the hybrid control strategy to stabilize the unstable periodic orbits by using small perturbations applied to the derived system. Numerical simulations are developed with Matlab software, not only to verify our theoretical results but also to show more complex dynamics of the derived model, including invariant curves and chaotic sets.

Platform-vibrator with shock is widely used in the construction industry for compacting and molding large concrete products. Its mathematical model corresponds to a two-body 2-DOF vibro-impact system with a soft impact. A soft impact is simulated with nonlinear Hertzian contact force. The choice of stiffness parameters greatly affects the model dynamic behavior. Some of their changes make it possible to increase the compaction efficiency. But the same changes in the stiffness parameters can lead to the emergence of undesirable and even dangerous nonlinear phenomena, such as chaotic motion, interior crisis, crisis-induced intermittency, transient chaos, and a hysteresis zone with coexisting regimes obtained for different initial conditions. The identity of the observed modes was confirmed by several methods. A performed detailed analysis of the influence of the platform-vibrator stiffness parameters at its dynamic behavior may be useful in the design and operation of this equipment. It can help to avoid the unwanted behavior because to the wrong choice of system stiffness parameters. Numerous Figures and Tables clearly and convincingly demonstrate the results of numerical studies.

In this paper, we propose a novel technique for the computer virus epidemic which contains infected external computer effects and removable storage media on the computer viruses. The positivity and boundedness for validation of the model are also discussed. The existence and uniqueness of the system of solutions for the model are made by using fixed point theory and iterative method. Numerical simulation obtained with proposed scheme which shows the impacts of varying the fraction-al-order parameters and the support of the theoretical results.

A healthy human body depicts variability to a large extent that can be easily described by using statistical algorithms. If this fluctuation arises occur in normal cycle of the heartbeat, it is called as heart rate variability (HRV). The rhythms of a normal and healthy heart continue to change every second with the metabolic activity that provides the heart and brain a new chance for changing and maintaining homeostasis according to variability. The aim of this research is to study long-term, short-term, and very short-term regulations of the body to cope with the condition of the heart as HRV changes. Time domain, frequency domain, non --linear dynamics are being overviewed. Where time-domain shows HRV changes during a time period of three minutes to one hour, frequency domain parameters illustrate the variation of data over an extended period of time. Nonlinear dynamics provides quantitative measurement of probability and biasedness in values obtained from the electrocardiograph. After careful investigation, it became clear as fact that short term i.e., mechanisms which are as less as five minutes and long term that are about one day cannot be correlated and can't be changed into one another. Moreover, the use of these statistical mechanics in clinical laboratories and therapeutics against myocardial infarction, blood pressure, and diabetes are elucidated in detail to gain access to potential generated by them during heart rate (HR) analysis to control morbidity rate effectively.

This work is concerned with the existence and controllability of impulsive stochastic integrodifferential systems with state-dependent delay in a real separable Hilbert space. The main results are obtained by using stochastic analysis theory, fixed point techniques and, Grimmer's resolvent operator theory. Finally, an example is provided to illustrate the proposed theory.

In this paper, we study well-posedness and asymptotic stability of a wave equation with a general internal control of diffusive type. We prove that the system lacks exponential stability. Furthermore, we show an explicit and general decay rate result. The method is based on the frequency domain approach combined with multiplier technique.

In this manuscript, we mainly focus on the existence and uniqueness of solutions for the Hadamard fractional neutral nonlinear Volterra-Fredholm integro-differential equation with infinite delay. We employ Krasnoselskii's fixed point theorem, Arzelá-Ascoli theorem and Banach contraction principle to show the existence and uniqueness of solutions of our problem. Lastly, we provide applications for the illustration of the obtained theoretical results.

In this paper, we establish some new conditions for the existence of solutions for a class of nonlinear Caputo fractional Volterra-Fredholm integro-differential equations with initial conditions. The desired results are proved by using Banach fixed point theorem for nonself mappings, fractional inequality and a version of the nonlinear alternative of Leray-Schauder in Banach spaces. Furthermore, the uniqueness results are established by the application of the contraction mapping principle. Finally, some examples are proposed to illustrate our main results.

In this article, sufficient conditions for the boundary controllability of semilinear impulsive Sobolev-type neutral integrodifferential functional evolution systems with timevarying delays in Banach spaces have been established. The results are obtained by using two-parameter family of evolution operators and fixed point theorem. An example is provided to illustrate the theory.