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Abstract The open nature of Wireless Sensor Networks (WSNs) renders them an easy target to malicious code propagation, posing a significant and persistent threat to their security. Various mathematical models have been studied in recent literature for understanding the dynamics and control of the propagation of malicious codes in WSNs. However, due to the inherent randomness and uncertainty present in WSNs, stochastic modeling approach is essential for a comprehensive understanding of the propagation of malicious codes in WSNs. In this paper, we formulate a general stochastic compartmental model for analyzing the dynamics of malicious code distribution in WSNs and suggest its possible control. We incorporate the stochasticity in the classical deterministic model for the inherent unpredictability in code propagation, which results in a more appropriate representation of the dynamics. A basic theoretical analysis including the stability results of the model with randomness is carried out. Moreover, a higher-order spectral collocation technique is applied for the numerical solution of the proposed stochastic model. The accuracy and numerical stability of the model is presented. Finally, a comprehensive simulation is depicted to verify theoretical results and depict the impact of parameters on the model’s dynamic behavior. This study incorporates stochasticity in a deterministic model of malicious codes spread in WSNs with the implementation of spectral numerical scheme which helps to capture these networks’ inherent uncertainties and complex nature.

The open nature of Wireless Sensor Networks (WSNs) renders them an easy target to malicious code propagation, posing a significant and persistent threat to their security. Various mathematical models have been studied in recent literature for understanding the dynamics and control of the propagation of malicious codes in WSNs. However, due to the inherent randomness and uncertainty present in WSNs, stochastic modeling approach is essential for a comprehensive understanding of the propagation of malicious codes in WSNs. In this paper, we formulate a general stochastic compartmental model for analyzing the dynamics of malicious code distribution in WSNs and suggest its possible control. We incorporate the stochasticity in the classical deterministic model for the inherent unpredictability in code propagation, which results in a more appropriate representation of the dynamics. A basic theoretical analysis including the stability results of the model with randomness is carried out. Moreover, a higher-order spectral collocation technique is applied for the numerical solution of the proposed stochastic model. The accuracy and numerical stability of the model is presented. Finally, a comprehensive simulation is depicted to verify theoretical results and depict the impact of parameters on the model's dynamic behavior. This study incorporates stochasticity in a deterministic model of malicious codes spread in WSNs with the implementation of spectral numerical scheme which helps to capture these networks' inherent uncertainties and complex nature. [ABSTRACT FROM AUTHOR]

In the present work, ZnFe2O4 and CoCr2O4 nanocomposites were prepared by the solution combustion synthesis method. The two materials were combined using the mechanical mixing method to produce nanocomposites with different weight ratios. The resulting nanocomposites were characterized by x-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), x-ray photoelectron spectroscopy (XPS), and zero-field-cooled (ZFC) and field-cooled (FC) magnetization. The XRD patterns confirmed the formation of a spinel structure, with average crystallite sizes of 35 nm and 20 nm, respectively. FESEM micrographs confirmed a non-spherical shape, homogeneous dispersion, and larger grain size. The XPS spectra were analyzed prior to determining the chemical composition of the (x)CoCr2O4 + (1−x)ZnFe2O4 materials, revealing the occurrence of each element that appeared nominally in the formula. The hysteresis M–H curves for all tested samples at 10 K demonstrated S-type behavior, confirming the ferro-/ferrimagnetic order. It was noted that for the CoCr2O4 sample, the M–H loop at 90 K exhibited linear behavior, confirming the paramagnetic order, with a Curie temperature (TC) of about 86 K. The experimental results indicate that the physical mixing process did not affect the phase purity of the nanoparticles, and the newly formed nanocomposites exhibited improved magnetic properties. [ABSTRACT FROM AUTHOR]