A fractal fractional model for computer virus dynamics

Akgül, Ali; Fatima, Umbreen; Iqbal, Muhammad Sajid; Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad

doi:10.1016/j.chaos.2021.110947

Cited by 14 publications

(9 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a different study, a powerful tool has been developed for all nonlinear models of biomedical engineering problems with the structural preservation method [19]. Akgül et al extended the classical computer virus model to the fractional fractal model in their study and then brought a solution to the model with the Atangana-Toufik method [20]. In a different study, the fractional order computer epidemic model was analyzed.…”

Section: Related Workmentioning

confidence: 99%

Novel Metrics for Mutation Analysis

Takan¹,

Katipoglu²

2023

Computer Systems Science and Engineering

View full text Add to dashboard Cite

A measure of the "goodness" or efficiency of the test suite is used to determine the proficiency of a test suite. The appropriateness of the test suite is determined through mutation analysis. Several Finite State Machine (FSM) mutants are produced in mutation analysis by injecting errors against hypotheses. These mutants serve as test subjects for the test suite (TS). The effectiveness of the test suite is proportional to the number of eliminated mutants. The most effective test suite is the one that removes the most significant number of mutants at the optimal time. It is difficult to determine the fault detection ratio of the system. Because it is difficult to identify the system's potential flaws precisely. In mutation testing, the Fault Detection Ratio (FDR) metric is currently used to express the adequacy of a test suite. However, there are some issues with this metric. If both test suites have the same defect detection rate, the smaller of the two tests is preferred. The test case (TC) is affected by the same issue. The smaller two test cases with identical performance are assumed to have superior performance. Another difficulty involves time. The performance of numerous vehicles claiming to have a perfect mutant capture time is problematic. Our study developed three metrics to address these issues: FDR TS j j , FDR TC j j , and FDR Time j j : In this context, most used test generation tools were examined and tested using the developed metrics. Thanks to the metrics we have developed, the research contributes to eliminating the problems related to performance measurement by integrating the missing parameters into the system.

show abstract

Section: Related Workmentioning

confidence: 99%

Novel Metrics for Mutation Analysis

Takan¹,

Katipoglu²

2023

Computer Systems Science and Engineering

View full text Add to dashboard Cite

show abstract

“…In the existing methods, the deterministic mathematical model with safety coefficients is often adopted to complete the structural design. A complex deterministic model like the fractal fractional model [1] can be built by computer modeling, but it cannot accurately describe the uncertainty in engineering problems. Stochastic extension of the deterministic model [2] can address the above issue; however, various assumptions are imposed to simplify the calculation, which limits this method.…”

Section: Introductionmentioning

confidence: 99%

Structural Interval Reliability Algorithm Based on Bernstein Polynomials and燛vidence Theory

Zhang¹,

Ni²,

Hu³

et al. 2023

Computer Systems Science and Engineering

View full text Add to dashboard Cite

Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors. Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid. The uncertain parameters mainly exist in the form of intervals. This method requires a lot of calculation and is often difficult to achieve efficiently. In order to solve this problem, this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty. Based on the non-probabilistic reliability index method, the extreme value of the limit state function is obtained using the properties of Bernstein polynomials, thus avoiding the need for a lot of sampling to solve the reliability analysis problem. The method is applied to numerical examples and engineering applications such as experiments, and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method, especially for some reliability problems with higher nonlinearity. Moreover, this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems.

show abstract

“…This leads to urgent requests for effective measures to prevent and control computer viruses and malware. For this purpose, many mathematicians and engineers have built mathematical models, which are based on epidemiological models and the high similarity of the spread of computer viruses and biological ones, to discover characteristics and transmission mechanisms of computer viruses and malware (see, for example, [3,13,15,19,20,21,40] and references therein). Consequently, effective measures to prevent and control computer viruses are suggested.…”

Section: Introductionmentioning

confidence: 99%

“…and study the GAS of the fractional-order model by using the present approach. It is worth noting that mathematical models using fractional derivatives have been widely used to describe phenomena and processes arising in theory and practice in recent years (see, for example, [3,6,9,11,13,39,43]) and the stability analysis of fractional-order models has been one of the most important problems in mathematical modeling and analysis [1,2,12,24,25,26,34,41,42]. By the present approach in combination with the Lyapunov stability theory for fractional dynamical systems, the GAS of the fractional-order model ( 26) is also established.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of integer-order and fractional-order malware spread models on WSNs

Hoang

2023

Preprint

View full text Add to dashboard Cite

In a recent work [J. D. Hernández Guillén, A. Martín del Rey, A mathematical model for malware spread on WSNs with population dynamics, Physica A: Statistical Mechanics and its Applications 545(2020) 123609], an integer-order model for the spread of malicious code on wireless sensor networks was introduced and analyzed. The global asymptotic stability (GAS) of the disease-endemic equilibrium (DEE) point was only resolved partially under technical hypotheses. In the present work, we use a simple approach, which is based on a suitable family of Lyapunov functions in combination with characteristics of Volterra-Lyapunov stable matrices, to establish the GAS of the DEE point. Consequently, we obtain a simple and easily-verified condition for the DEE point of the integer-order model to be globally asymptotically stable. In addition, we generalize the inter-order model by considering it in the context of the Caputo fractional derivative. After that, the proposed approach is utilized to analyze the GAS of the fractional-order model. The result is that the GAS of the DEE point of the fractional-order model is also established. As an important consequence, the advantage of the present approach is shown. Finally, the theoretical findings are supported by numerical and illustrative examples, which indicate that the numerical results are consistent with the theoretical ones. 2010 MSC: 34C60, 34D05, 33C75, 37N99

show abstract

A fractal fractional model for computer virus dynamics

Cited by 14 publications

References 30 publications

Novel Metrics for Mutation Analysis

Novel Metrics for Mutation Analysis

Structural Interval Reliability Algorithm Based on Bernstein Polynomials and燛vidence Theory

Stability analysis of integer-order and fractional-order malware spread models on WSNs

Contact Info

Product

Resources

About