Vol. 15, No. 1 (2026): Regular Issue

There have sometimes been reports of an influence of behavioral reactions and awareness campaigns on epidemic breakouts. From a public health perspective, knowledge and behavioral changes are crucial, but it is unclear how much they affect the course of the pandemic. Using a mathematical model, we explore the impact of media awareness efforts on the onset of asthma in a population that is genetically susceptible to pollution. Assessments are made of the system's durability and the prerequisites for the existence of the unique positive stable state. Lyapunov's function analysis identifies the unique positive steady state as being both locally and globally asymptotically stable. Campaigns to raise awareness can help prevent the expansion of the asthma pandemic, but immigration maintains the condition endemic, according to the model research. The model is also numerically analyzed to confirm the analytical results and ascertain how many important parameters affect the asthma outbreak.

This paper proposes a modified multivariate permutation entropy (MPE) algorithm to quantify the complexity of the multi-dimensional time series. The novelty of the algorithm lies in a multivariate ordinal pattern representation which requires a significantly smaller number of combinations of obtained multivariate ${d}$-order permutations for ${m}$-dimensional time series, comparing the direct application of a univariate permutation entropy to the multi-dimensional time series and resulting in the value of $d!{}^{m}$ combinations. More specifically, the number of combinations of multivariate ordinal patterns is reduced to $d!{}^{k}$ with ${k}<<{m}$ by obtaining the patterns from k-dimensional time series, randomly selected with multiple repetitions from the ${m}$-dimensional time series. The final distribution of the multivariate ordinal patterns is obtained by the summation of these patterns across all repetitions. The capabilities of the proposed method are verified based on numerical experiments and empirical multidimensional data sets. The method is specifically applied to i) a multivariate deterministic system (a network of ten chaotic Rössler oscillators diffusively coupled to their nearest neighbors); ii) a multivariate noise field that is colored in space and white in time; and iii) multi-channel electroencephalogram (EEG) recordings.

In this paper, a novel 4-D hyperjerk system with one stable equilibrium at the origin is presented. The system is constructed via a specific procedure and the stability of the equilibrium is determined by Routh-Hurwitz criterion. Numerical investigation of the system by using the bifurcation diagram, phase portraits, Lyapunov exponents and basins of attractions uncovers its chaotic dynamics and multistability. Also, the projection method of Kuznetzov is followed in order to study the Hopf bifurcation of the system. In addition, a pseudorandom bit generator is introduced. The pseudorandom bit sequence is generated by a chaotic solution of the system and the randomness of the bitstream is confirmed by NIST 800-22.

This paper provides a detailed overview of the meteorological conditions that led to persistent heavy rainfall events and subsequent flooding in parts of Maharashtra during July 20-24, 2021. Meteorological factors such as an off-shore trough, a shear zone, a cyclonic circulation over south Gujarat, and a Low Pressure Area (LPA) over the Northwest Bay of Bengal (BoB) were identified as favorable environmental conditions. The combination of these factors created an environment conducive to persistent heavy rainfall over Maharashtra. The off-shore trough, shear zone, and cyclonic circulation facilitated moisture convergence and uplift, resulting in widespread rainfall. Additionally, the presence of the LPA intensified moisture influx and atmospheric instability, amplified the intensity of the rainfall event. The trough associated with the cyclonic circulation of the LPA acted as a moisture channel, allowing moisture transport from both the Arabian Sea (AS) & BoB to Maharashtra. Favorable dynamical conditions, such as lower level convergence (LLC) and upper level divergence (ULD), further supported persistent heavy rainfall weather events over the region. Understanding these meteorological conditions is essential for forecasting and mitigating the impacts of extreme weather events like heavy rainfall and flooding. Analyzing the atmospheric dynamics and synoptic patterns associated with such events enables meteorologists to enhance early warning systems and provide timely information to help communities prepare for and respond to such situations effectively.

Neighbor maps of an iterated function system (IFS) were studied and analyzed to characterize the points that lie in the feasible open set satisfying the open set condition. The global neighbor set (GNS) of an IFS is defined using the images of neighbor maps on the attractor. Results are presented on how the overlap between the attractor and the neighbor set of an IFS relates to the open set condition of the IFS are presented. GNS of condensation IFSs are studied using the corresponding homogeneous IFS, and related results are obtained. In product spaces, GNSs are studied, and their inverse invariance properties are characterized. The Hausdorff dimension of the GNS is also calculated. The property of GNS to identify regions where different function maps overlap on the attractor makes it a tool to detect the boundaries of regions in an image, proposing it as an application in edge detection.

In this paper, we extend ordinary differential equations to Caputo-type differential equations and apply optimal control theory to explore how control strategies can be implemented over a fractional order to reduce the number of active infected individuals while minimizing intervention costs. We demonstrate the criteria for the existence and uniqueness of the proposed model and examine the non-negativity and boundedness of the solutions. Additionally, we analyze the basic reproduction number and its sensitivity. We study the stability criteria for both the disease-free and endemic equilibrium to understand the qualitative behavior of the model. The proposed mathematical model incorporates three control terms, and using the Pontryagin Maximum Principle, we analytically derive the optimal control characteristics of the model. The analytical results are supported by numerical analysis and simulations, which demonstrate the most effective control of the intervention.

In this article, the mechanic analysis of Burke-Shaw system have been studied. Firstly, the system is transformed into Kolmogorov type system and further decomposed into four types of torques: inertial torque, internal torque, dissipation torque and external torque. Five scenarios are examined using combinations of various torques in order to identify the key elements for chaos creation and their physical significance. In these scenarios, the conversion between kinetic energy, potential energy and Hamiltonian energy are examined. The interaction between energy and the parameters is also explored. The conclusion reveals that any combination of three forms of torques can not create chaos in Burke-Shaw system but a combination of four types of torques concrete it.

The work resolves around the analysis of Ulam-Hyers stability and Ulam-Hyers-Rassias stability of Conformable fractional order control system. Initially, we utilize the concept of trigonometric functions such as sine and cosine to define the Conformable matrix to deduce the sufficient conditions for the system to admit stability. The theoretical study is authenticated by providing appropriate numerical simulation.

In this paper, impulsive periodic motions in a pendulum under sinusoidal impulses are studied through the implicit mapping method. From the specific mapping structures, the periodic motions in the sinusoidally impulsive pendulum are obtained, and the stability and bifurcation of the corresponding impulsive periodic motions are analyzed. The bifurcation trees of the impulsive periodic motions to chaos are presented, and the impulsive homoclinic orbits are also obtained. The impulsive homoclinic orbits are for the homoclinic bifurcations of the impulsive periodic motions. The impulsive periodic motions and impulsive homoclinic orbits of the pendulum under sinusoidal impulses are illustrated. Such a method can be extended to the switching system with transport laws.