This work investigates exact travelling-wave solutions of a non-dissipative double-dispersive strain-wave equation describing nonlinear wave propagation in microstructured solids. The Bogning--Djeumen--Tchaho--Kofane method extended to implicit Bogning functions is applied to construct and classify admissible analytical wave profiles of the model. By using a travelling-wave transformation, the governing nonlinear partial differential equation is reduced to an ordinary differential equation, which is then treated through an implicit Bogning-function ansatz. The substitution procedure leads to a coefficient-range equation whose admissible index pairs and parameter constraints determine the possible solution branches. A key aspect of the analysis is the direct verification of the obtained amplitudes: only branches for which all collected coefficients vanish identically are retained as exact solutions. The resulting verified solutions include hyperbolic and trigonometric forms. The hyperbolic branches describe non-periodic travelling structures such as localized, singular localized, regular pulse-type, and dark-soliton-like profiles, whereas the trigonometric branches represent periodic or singular periodic propagation regimes. Graphical representations are provided to illustrate the influence of the admissible parameter constraints on the shape, localization, and propagation of the waves. The results show that the extended BDKm framework offers a systematic coefficient-based approach for deriving, verifying, and classifying exact wave solutions in double-dispersive microstructured media. The obtained profiles may serve as benchmark solutions for future numerical simulations, stability studies, and parameter-sensitivity analyses of nonlinear strain-wave dynamics.
A heterogeneous two-server queueing system with differentiated vacations and server failures is examined in this paper. The matrix geometric method was applied to identify the system's stationary condition by analyzing the steady-state probability distribution of customer numbers, modeled as a quasi-birth-and-death (QBD) process. A few metrics regarding system performance are acquired. Graphs and tables illustrate how parameters affect performance metrics. Transient numerical analysis is given for the proposed model using RK method.
This paper deals with the existence of traveling wave solutions of Fisher equation with a shifting habitat representing a transition to a devastating environment. By constructing a pair of appropriate upper/lower solutions and using the method of monotone iteration, we prove that for any given speed of the shifting habitat edge, this reaction-diffusion equation admits a monotone traveling wave solution with the speed agreeing to the habitat shifting speed, which accounts for an extinction wave. This predicts not only how fast but also in what manner a biological species will dies out in such a shifting habitat.
. Chaotic property of dynamical systems is known to be exploited in image encryption scheme. In this paper, we study the chaotic property of a fractional order logistic map with feedback control, additive Allee effect, and harvesting. Dynamical analyses are discussed such as the existence and local stability of fixed points of the map. The study also establishes the existence of Neimark-Sacker and period-doubling bifurcation. With the intention to enhance the chaos complexity of the map, we modify the map by utilizing the cascade concept and modulo operation to become the fractional-order modified logistic map (FOMLM). Chaos complexity is analyzed with bifurcation diagram, chaos trajectories, and Lyapunov exponent. Subsequently, a FOMLM-based color image encryption scheme is proposed to establish the "permutationdiffusion" concept in the encryption scheme. Performance analysis of the scheme gives an indicator of robustness against cryptanalysis and is highly sensitive to the plain image and the secret key.
Technological development brought the risk of networks being threatened by computer viruses which led to data breaches and financial losses for companies. To mitigate this risk, insurance products were offered to protect against these virus spread attacks. This epidemic phenomenon was modeled using both the Susceptible-Infected-Recovered-Susceptible compartment model and the Markov model. The estimated population from the SIRS model was used as dataset for the distribution fitting process within the Markov model. The estimated parameters were used for simulations to calculate the upper bound infection and stationary probabilities, the number of infection events, and the resulting financial losses. From these losses, the insurance premium was estimated using the standard deviation calculation principle. The results showed that the SIRS model and the Markov model had similar characteristics, allowing for distribution fitting, specifically the infection and recovery processes. The upper bound infection probability obtained from the simulation was used to estimate the likelihood of claims resulting from virus infections. The insurance premium value for the risk of networks being attacked by computer viruses was grouped based on the antivirus performance of the computer network, determined through the underwriting process.
