Modulational instability of a plane-wave mode is known to lead to spontaneous energy localization in nonlinear lattices without the presence of impurities. Where the energy dynamically localizes in the system is highly sensitive to initial conditions. Here we numerically investigate sine-Gordon-type lattices and first show that spatial smoothing of the observed dynamical variables on the lattice can already substantially improve predictions of the eventual localization site from early-time data traces alone, suggesting that the type-III instability that forms the energy hotspot is sensitive to energetic clusters. We then show that machine learning leads to additional dramatic improvement in prediction accuracy. Finally, we also examine the role of chain impurities in determining the localization site.

Smoking is a leading cause of death due to its detrimental effects on various organs, leading to strokes, heart diseases, and other respiratory issues. This paper presents a mathematical model to examine the dynamics of smoking and the recovery rate within a community. The model employs a compartmental approach, consisting of five non-linear differential equations, to analyze these dynamics. Both the local and global stability of the model are investigated. Additionally, the next-generation matrix technique is utilized to perform an in-depth analysis based on the reproduction number $R_0$, which is calculated using Python. Several numerical simulations are conducted to illustrate the findings, highlighting the impact of various parameters on smoking dynamics and the effectiveness of intervention strategies.

Mathematical modeling has become an essential theoretical tool for understanding fundamental aspects of various medical and biological phenomena. This paper develops a mathematical model involving the incomplete $H$-function (I$H$F). The primary objective of this study is to analyze the glucose supply in human blood. The results are comprehensive and emphasize the impact of key parameters on glucose dynamics. These findings uncover intricate relationships between glucose supply and metabolic processes. The model provides a robust framework for exploring scenarios that replicate real-world physiological conditions, highlighting its potential applications in diabetes management and metabolic research.

This article explores a Fredholm-type integral equation featuring an incomplete $\aleph$-function in its kernel, with implications for solving real-world problems representing diverse physical phenomena. Employing fractional calculus and Mellin transform principles, we address an integral problem involving the incomplete $\aleph$-function. The Mellin transform and fractional calculus are subsequently applied to analyze an integral equation using the incomplete $\aleph$-function. Various significant exceptional cases have been identified and scrutinized. The general insights from this article may lead to the formulation of new integral equations and solutions, contributing to the resolution of practical challenges.

This paper studies the bifurcation of limit cycles for a specific predator-prey model called Rosenzweig-MacArthur, that presents persistent oscillations in the amount of individuals of the population from predator group and from the prey group. This model uses a Holling Type II function response. The averaging theory of third order allows to investigate the Hopf bifurcation that exhibits this model, providing an analytical approximation of the bifurcated periodic orbit and its kind of stability.

This paper introduces a new12-term six-dimension, continuous hyperchaotic system derived from the 4D Ma system by merging coupling and linear state feedback control strategies. This system has four positive Lyapunov exponents (LEs) with a non-hyperbolic unstable saddle equilibrium point. It demonstrates various dynamic characteristics, including periodic, quasi-periodic, chaotic, and hyperchaotic. Furthermore, the system is translated into an analog electronic circuit and simulated using an oscilloscope device, showing consistency between MATLAB 2023 and Multisim 14.3 software simulations.

The present study applies functions of new cubic B-splines to compute numerical solutions for the modified time fractional Burgers equation using the $\theta $-weighted scheme, employing time fractional derivative using the Caputo fractional order derivative. The finite difference method is employed for the discretization of time, while the cubic B-splines are used for spatial discretization. The quasi-linearization technique was employed to linearize the nonlinear term in the given fractional differential equation. The effectiveness of the proposed method was tested on one specific problem, with the impact of viscosity $\mu$ and parameter $\beta\in(0,1]$ depicted through 2D and 3D graphs. An algorithm is used to explain the suggested approach, the von Neumann technique was employed to analyze the stability of the suggested scheme, which was found to be unconditionally stable. The second-order convergence of the scheme in both spatial and temporal directions has also been discussed and confirmed. To evaluate the accuracy of the proposed scheme, error norms have been calculated and examined.

This paper explores a novel dual synchronization method for fractional-order complex-valued neural networks (FOCVNN) by combining adaptive control, inequality techniques, and stability theory of fractional calculus. The FOCVNN are separated into two real-valued parts and two imaginary-valued parts. According to the proposed dual synchronization scheme, a chaotic masking method is suggested for encrypting medical images to preserve patient information. Simulation results demonstrate the efficiency of the control laws and parameter updating equations. Additionally, experimental results including histograms, change rate of the number of pixels in the cipher-image (NPCR), unified average changing intensity (UACI), peak signal-to-noise ratio (PSNR) and correlation confirm the effectiveness of the proposed method for secure image communication.