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The main aim of this paper is to analyze a mathematical model for malware dissemination on wireless sensor networks with time delay. Local stability and exhibition of the Hopf bifurcation are explored by means of analysis of the distribution of roots of the consequential characteristic equation. Moreover, global exponential stability is established with the help of linear matrix inequality techniques. Furthermore, properties of the Hopf bifurcation such as the direction and stability are studied by utilizing the normal form theory and the center manifold theorem. Finally, a computer numerical simulation example is presented to certify the rationality of our obtained results. [ABSTRACT FROM AUTHOR]

In the cultivation of Capsicum annuum (C. annuum), the major obstacles are triggered by the Yellow virus (Gemini virus). The virus is spread through insects, namely Bemisia tabaci (B. tabaci). To reduce the spreading of the virus in C. annuum, the entomopathogenic fungi (Verticillium lecanii) are used. We have analyzed the fractional-order model of chili plants with Atangana–Baleanu derivative (AB-derivative). Also, we calculate the numerical values to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical semi-analysis of the delayed food chain model under the considered fractional order. The food chain model is composed of three compartments, namely, population of the prey, intermediate predator and a top predator. By using the fixed point theorem approach, we exploit some conditions for existence results and stability for the considered system via Atangana–Baleanu–Caputo derivative with fractional order. Also, using the well-known Adam–Bashforth technique for numerics, we simulate the concerning results for the interference between the prey and intermediate predator. Graphical results are discussed for different fractional-order values for the considered model. [ABSTRACT FROM AUTHOR]