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Today, with real-life problems, modeling is a primary step in organizing, analyzing and optimizing them. Queueing theory is a particular approach used to model this category of issues. Space constraints, feedback, service dependency, etc. are often inseparable from the issues they create. In light of this objective, this research presents a model and analysis of the steady-state behavior of an $M/G/1$ feedback retrial queue with two dependent phases of service under a Bernoulli vacation policy. The service times for the two stages are often independent in normal queueing frameworks. We presume that they are dependent random variables in this case. Indeed, this dependence is one-way (i.e., the service time of the second phase has no effect on the service time of the first phase). Yet, the first phase service time has an impact on the second phase service time. In order to determine the steady-state probabilities and probability-generating functions (PGF) for the different states, the supplementary variable technique (SVT) was utilized. Furthermore, a broad range of performance metrics had been established. The generated metrics are then envisioned and validated with the aid of graphs and tables. Additionally, a nonlinear cost function is constructed, which is subsequently minimized by distinct approaches like particle swarm optimization (PSO), artificial bee colony (ABC) and genetic algorithm (GA). Furthermore, we used certain figures to examine the convergence of these optimization methods. Finally, validation outcomes are compared with neuro-fuzzy results generated with the “adaptive neuro-fuzzy inference system” (ANFIS).

In this paper a chaotic system is proposed via modifying hyperchaotic Chen system. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic behaviors of this system are studied. The conventional feedback, linear function feedback, nonlinear hyperbolic function feedback control methods are applied to control chaos to unstable equilibrium point. The conditions of stability to control the system is derived according to the Routh–Hurwitz criteria. Numerical results have shown the validity of the proposed schemes.

Cells are continuously subjected to noisy internal and external environments. Though cellular functions are carried on quite reliably under such noise, they can also result in fluctuations of parameters of the various biochemical processes and cause the dynamics of the reaction pathway to change. To show the varied effects of noisy environment on cellular dynamics, we consider a model cell containing a minimal biochemical pathway that exhibits a wide array of dynamical behaviors – from equilibrium, simple limit cycles and higher periodics, birhythmicity, complex oscillations and chaos - that are observed in many cellular functions. We show that, even under constant parameters, small fluctuations in the variables (i.e., substrate concentrations) can facilitate switching of the dynamics between oscillatory states with very different amplitudes and frequencies. The final temporal behavior of the pathway is unpredictable for the range of parameters where birhythmicity is observed. Parametric noise can mask the original dynamics of the pathway in the birhythmic state, though considerable robustness in dynamics is seen in the presence of noise for other values of parameters. Thus we show that the cellular dynamics can exhibit both robust and non-robust behavior in noisy environment for different parameters in the same pathway.