Muhammad Junaid Ali Asif Raja

Industrial Internet of Things (IoT) is a revolutionary paradigm that bridges legacy industrial infrastructure and advanced digital innovation to enhance operational proficiency, data-driven decision making, and intelligent automation. Programable Logic Controller (PLC) serves as a key pillar of industrial automation, vulnerable to becoming a target vector for cybercriminals to infiltrate industrial systems through malware dissemination in industrial network ecosystem. This study explores the fractional-order nonlinear industrial worm spread time delay (Fr-NIWS-TD) model in PLC-enabled industrial control networks by leveraging nonlinear multilayer autoregressive exogenous network (NM-ARXN) aided with Levenberg-Marquardt (LM) backpropagation, i.e., NM-ARXN-LM neuroarchitecture. The Adams-Bashforth-Moulton predictor-corrector scheme with Caputo fractional operator is efficaciously employed to simulate the system scenarios that act as a synthetic data for NM-ARXN-LM framework to address the Fr-NIWS-TD model with distinct dynamic state variables of Susceptible S, Infected I, Halted H, Quarantine Q, and Recovered R, (SIHQR) nodes for worm transmission in industrial IoT infrastructure. The methodically structured simulation analysis conducted on sundry Fr-NIWS-TD case-studies such as varying (i) the rate of quarantine node converting to recovered node along with the likelihood that its operational device program blocks are rewritten by updated programs, (ii) the rate of a recovered node losing its immunity R to S node, (iii) shutdown (halting) rate of an infected node induced by worm I to H node, (iv) quarantine rate I to Q node, (v) the rate of intrusion detection system (IDS) effectively interrupting worm spread during a unit time interval. The Fr-NIWS-TD simulation datasets, to be modeled by the intelligent computing paradigm, are stratified into training, validation and testing subsets. The proposed NM-ARXN-LM technique’s proficiency is endorsed through comprehensive performance evaluations on mean squared error (MSE) convergence trends, error distribution histograms, correlation evaluation, regression analysis, and time-series fitting patterns, while the structural integrity and convergence stability of neuroarchitecture are further substantiated through numerical comparative analysis with absolute error distribution plots. Extensive evaluations on single-step and multi-step ahead horizons with MSE of order 10-11 to 10-14, empirically underscores robustness, resilience and high-fidelity approximation competence of the NM-ARXN-LM methodology in capturing the complex worm propagation dynamics in Industrial IoT networks.

Memristive neuronal architectures constitute sophisticated dynamical systems that exhibit complex nonlinear spiking phenomena through the synergistic integration of memory-dependent conductance modulation and intrinsic neuronal dynamics. This investigation elucidates the emergent behavioral manifestations of a Locally Active Memristive Neuron (LAMfrefeN) paradigm, synthesized through the amalgamation of a two-dimensional Hindmarsh-Rose neuronal substrate with an autaptic memristive element exhibiting locally active characteristics. In this paper, this dynamical framework undergoes systematic transformation into a fractional-order paradigm through the rigorous implementation of the Caputo fractional differential operator, namely the Fractional Locally Active Memristive Neuron (FLAMN) model. Numerical integration of the Fractional-order system is accomplished via the Adams-Bashforth-Moulton Predictor-Corrector (FABM-PrCr) computational methodology. Fractional-order derivatives inherently incorporate non-local hereditary memory effects, substantially enhancing the system’s representational fidelity in capturing the intricate temporal dynamics and long-range dependencies characteristics of biological neurons. The proposed FLAMN configuration demonstrates quintessential neuronal excitability patterns encompassing periodic bursting, periodic spiking, chaotic bursting, chaotic bursting and stochastic bursting firing regimes, thereby recapitulating the multifaceted electrophysiological repertoire observed in biological neural architectures. Subsequently, an intelligent computational framework is designed to function as a sophisticated surrogate system for the FLAMN model, by means of a Hybrid Non-Linear AutoRegressive Neural Network backpropagated through Levenberg-Marquardt (HNLARXNN-LM) algorithm. The forecasting and modeling prowess of the diverse firing patterns of the FLAMN is done through diverse error analysis on singular and multi-step ahead horizons, error histogram, correlation and regression analysis. Empirical results demonstrate mean squared errors in the ranges of 10-9-10-11. The FLAMN dynamical systems reconstruction by NLARXNN is visually apprehended through comparative time-series and absolute error evolution curves. With reconstruction error as low as 10-3-10-6, we showcase that the developed FLAMN framework demonstrates exceptional consistency in reproducing the intricate temporal dynamics and statistical properties of the memristive neuron, establishing a robust foundation for subsequent investigations into neuromorphic computing applications and theoretical neuroscience endeavors. An inference study on completely unseen FitzHugh-Nagumo spiking dynamics further validates this claim, with reconstruction errors in the ranges of 10-5 to 10-7, showcasing apt cross-generalizability and effectiveness of the HNLARXNN-LM as a surrogate differential solver.

In aquatic ecosystems, the triadic relationship among phytoplankton, zooplankton, and their piscine predators constitutes a delicately balanced ecological continuum where nutrient cycling, toxin transfer, and spatial refugia collectively dictate population persistence and the wider vitality of marine communities. In this paper, the fractional-order dynamics of Nekton-Plankton Coupled (N-PC) systems are analyzed using intelligent computing driven autoregressive exogenous artificial neural networks (ARX-ANNs). Initially, fractional N-PC dynamics under toxicity, refuge and nutrient flux constrains are time-evolved using an efficient Adams-Moulton-Bashforth predictor corrector method incorporating the Caputo fractional operator. These diverse scenarios are subsequently fed into the ARX-ANNs that are efficiently trained by means of a hybrid second order Bayesian Regularized Levenberg Marquardt optimization algorithm. The efficiency of the intelligent computing regime in modeling and forecasting the complex dynamics of the N-PC model is comprehensively evaluated against reference simulations using mean squared error convergence curves, time-series response analysis, correlation charts (for autoregressive models), error frequency distributions, and regression reports. Comparative analysis between the traditional numerical approach against the ARX-ANNs demonstrates remarkably low errors in the ranges of 10-04 to 10-12. To further assess the robustness of the proposed methodology, step ahead forecasts of single and multiple prediction horizons are explored, and validated with low errors on the order of <10-13. Results show that the intelligent neuro-computing surrogate can effectively delineate the ecological spatiotemporal dynamics and population trajectories in complex marine food webs.

The incredible synergy between monoclonal anti- bodies and interferons in cancer chemotherapy signifies a stride forward in our battle against this inexorable disease. Through meticulous mathematical modeling that delineate the interplay between tumor growth and immune response, this helps in the development of immunomodulatory treatments and aids in counteracting the cost of drug discovery while minimizing the resource-intensive experimental iterations. This study develops a precise and reliable application of numerical as well as artificial intelligence-based treatment methodology via predictive super- vised eXegenious networks for calculable understanding of the movement of the immune response to treatment such as timing, dosing and forecasting therapy retorts to a specific dose. The out- comes of this work underscore the potency of these methodologies in clarifying the pivotal determinants essential to the dynamic of tumor-immune interactions, therapeutic efficacy and the for- mulation of rationalized therapeutic interventions. In the pursuit of unraveling the complexities inherent to the interactions within the tumor-immune-chemotherapy model, this study harnesses the predictive power of nonlinear autoregressive exogenous (NARX) networks, synergistically coalesced with stochastic-deterministic differential modeling, to unfold the hidden intricacies that hold significant potential within this intricate process. Reference data for training, testing and validation of the proposed methodology was generated using Adams numerical method by utilizing baseline parameters derived through experimental data. Error analysis was conducted to verify the authenticity and perfor- mance of the designed framework for different scenarios. The framework demonstrates impressive performance and accuracy, achieving a mean square error between 10^-11 and 10^-8 through iterative refinement.

The Rabinovich–Fabrikant system epitomizes a fundamental construct in nonlinear dynamical systems, where subtle parametric interplays lead to the emergence of intricate chaotic attractors, and an exceptionally sensitive dependence on initial conditions within multifaceted physical contexts. In this paper, we present a fractional-order Rabinovich–Fabrikant (FO–RF) system demonstrating chaotic attractor-like behavior under different fractional orders and parameter sets. This characterization is achieved through a twofold approach: first, an efficient Caputo fractional differentiation-based Adams multistep PECE solver is incorporated to numerically treat the nonlinear FO-RF systems; second, a nonlinear AutoRegressive eXogenous (ARX) temporal neuro-structure is devised to simulate, analyze and characterize the ensuing chaotic dynamics. The numerical outcomes are prepared for the nonlinear ARX neural network characterization through a time-based partitioning into training, validation and testing sets, with optimized temporal feature learning through a Bayesian Regularized Levenberg Marquardt backpropagation (BRLM-BP-ARX) algorithm. These predicted sequences are rigorously evaluated against their numerical counterparts with analysis on iterative error convergence charts, regression reports, correlation infographics, and sequential temporal responses. Additionally, a thorough comparative error analysis for the simulated FO-RF solutions is carried out. To further assess the temporal feature learning robustness, the BRLM-BP-ARX neural network’s one-step-ahead and multi-step-ahead forecasting capabilities are tested for the intricate FO-RF chaotic dynamics. The empirical results from exhaustive experiments showcase that the BRLM-BP-ARX framework attains diminutive errors, spanning from 10–7 to 10–12, underscoring effectiveness of the approach for intricate fractional-order nonlinear dynamical systems.

The Hindmarsh-Rose (HMR) model, widely regarded as a cornerstone in the field of computational neuroscience, distills complex neuronal dynamics into a tractable framework capable of reproducing diverse firing patterns – ranging from tonic spiking to bursting and chaotic dynamics – while maintaining an essential balance of biological plausibility and mathematical simplicity for the exploration of neuronal excitability, synaptic interactions, synchronization patterns and emergent network-level phenomena. This paper presents the fractional-order extension of the HMR neuronal model, demonstrating a diverse range of firing behaviors, including slow spiking, chaotic bursting, fast spiking, Type I and Type II bursting, and chaotic spiking. The fractional HMR neuronal models’ spatiotemporal dynamics are numerically simulated using an efficient Caputo Fractional Adams-Bashforth-Moulton Predictor-Corrector (FABM-PECE) solver. A novel Nonlinear AutoRegressive eXogenous Neural Network enhanced with hybrid second-order Levenberg Marquardt optimization algorithm (LMNARXNNs) is designed to delineate, analyze and simulate the fractional HMR neuronal models. A comprehensive experimental investigation is conducted to compare the proposed intelligent computing technique with reference HMR solutions. This proposed neural network strategy undergoes extensive analysis using iterative performance curves (MSE) for training, testing and validation, along with error autocorrelation, error histograms, regression analysis and correlation examinations between exogenous inputs and errors. Through comparative graphical illustrations and absolute error evaluations between the LMNARXNN and FAMB-PECE solutions, it is observed that LMNARXNN encapsulates each fractional HMR neuronal model impeccably with error evaluations in the ranges of 10-02 to 10-05. Further scrutiny on 1-Step and multi-step (5-Step) predictions, with errors on the order of 10-07 to 10-09, validates the robustness and precision of the LMNARXNN approach in accurately delineating the intricate fractional HMR firing patterns. These findings underscore that the LMNARXNN strategy constitutes a highly accurate methodological framework for modeling and forecasting neuronal dynamics, firing patterns, excitability transitions and complex temporal structures.

Within the tranquil confines of air-gapped environment, the custodians of digital fortitude must recognize the limitations of a singular defense mechanism, the cornerstone of this defensive architecture lies in proactive threat detection and rapid response capabilities. In the presented study, a deep-learning based bidirectional LSTM architecture is designed to accurately capture the time-delay differential propagation dynamics of the Stuxnet virus in an air gapped environment intricately linked with a network of critical control infrastructure. To address the challenges encountered in compromising the air gapped environment, the mathematical model introduces time delay factors \tau_1, \tau_2 and \tau_3, necessary for exploiting the susceptible USB media, susceptible air gapped computers utilizing infected USB media and connected susceptible computers using infected computers respectively. Removable storage media serves as a pivotal link in bridging the air gapped environment and controlling the industrial controllers connected to critical systems thereby posing a significant threat to the integrity of the entire system. Synthetic temporal simulations serve as the ground truth for dual-layer bidirectional LSTM networks exactment on various scenarios involving the infiltration of the air-gapped environment by the Stuxnet virus in a time delay differential system. A detailed comparative analysis with numerical outcomes showed minimal disparity between the predictions generated by LSTM networks, with mean squared error (MSE) values falling within the range of 10-7 underscoring the effectiveness, robustness, and stability of the proposed neural networks in predicting the complex dynamics of virus in air gapped situation.

In this study, design of cascaded feedforward neural network optimized with Bayesian Regularization algorithm is deployed to study the nonlinear fractional order system of carbon-thermal nutrient-plankton model asserting the profound ramifications of global warming and climatic alterations on the planktonic populations within the marine biosphere. The fractional differential asymmetric multifactor system is reflected by the carbon dioxide atmospheric concentration, atmospheric temperature, nutrient concentration and planktonic population spatiotemporal dynamics in the ocean. This system is exacted by an efficacious variant of the fractional Adams-Bashforth-Moulton predictor-corrector method across distinct scenarios and fractional orders. These numerically treated datasets are subsequently partitioned into training and testing subsets to model the intricate dynamics of the fractional Plankton system using the cascaded intelligent computational paradigm. The stupendous knacks of the cascaded network framework are evaluated on the sundry fractional nonlinear carbon-thermal nutrient-plankton model scenarios using mean squared error convergence pattern, input-error correlation and error autocorrelation statistics, regression metric, time series response curves, and error histogram studies. The efficacy of the designed cascaded feedforward networks modelling is substantiated by diminutive training mean square error discrepancies, spanning from 10-11 to 10-15 across all the complex nonlinear fractional plankton cases. Furthermore, comparative analysis and absolute error visualizations reveal that the designed neural strategy effectively delineates the carbon-thermal nutrient-plankton dynamics as evidenced by the errors spanning from 10-05 to 10-08. These empirical results showcase that the neurocomputing strategy is robust in characterizing the intricate and complex nutrient-plankton dynamics in marine ecosystems under global warming and climatic perturbations.

Artificial intelligence has transformed both plankton dynamics and hazardous material management under toxic environments by enhanced hazard prediction in detecting how toxins affect plankton population and potentially uncovering greater depth of ecological insights. In proposed study, nonlinear autoregressive exogenous neural network coupled with Levenberg-Marquardt is efficaciously selected to model fractional order toxin plankton (FOTP) system asserting the phytoplankton and zooplankton dynamics in aquatic environment under influence of environmental toxins. The fractional differential ecological TP system incorporates density population of phytoplankton, zooplankton and environmental toxins exacted by fractional Adams multistep predictor-corrector method across arbitrary fractional order cases varying intrinsic growth rates of phytoplankton and zooplankton, zooplankton carrying capacity, phytoplankton toxin release, fish predation parameters (half-saturation constant and maximum rate), environmental toxin depletion, and dynamic phytoplankton carrying capacity. Synthetic datasets were split into training, testing, and validation subsets to model the FOTP system using an intelligent neurocomputing paradigm. The proficiency of the selected neural networks is demonstrated by performance metrics – MSE convergence, time-series fitness patterns, regression reports, error histograms and correlation analyses – while comparative analysis with numerical outcomes and absolute error plots underscores the robustness and stability of the neurocomputing architecture. Rigorous analysis on single step and multistep ahead predictors with error of order 10-5 further highlights the efficacy of employed neurocomputing design for optimal and precise forecasting of intricate FOTP system dynamics. This study demonstrates that intelligent computing can effectively forecast FOTP dynamics and serve as a framework for addressing aquatic ecological hazards.

The electrophysiological modelling paradigm unravels the complex oscillatory and excitable behaviors inherent to neural dynamics, with the FitzHugh-Nagumo model – rooted in the reductionist abstraction of Hodgkin-Huxley formalism – providing a quintessential framework for exploring the underpinnings of action potential propagation and diverse phase plane dynamics characterizing excitable membranes. The objective of this study is to present the novel intelligent computing-based Bayesian regularized multilayered deep dual cascaded nonlinear autoregressive exogenous neurostructure to model and predict the intricate dynamics of FitzHugh-Nagumo model. The numerical treatment of the FitzHugh-Nagumo (FHN) model is handled with a modified Adams-Bashforth-Moulton predictor-corrector method for three sundry scenarios encompassing the oscillatory, excitable, and bistable dynamics. These simulated temporal sequences are arbitrarily divided into training and test sets for Deep Cascaded NARX neural networks, with backpropagated refinement using the Bayesian regularization technique (DC-NARX-BR). This novel strategy is verified across reference numerical outcomes with the help of diversified evaluation metrics including mean squared error convergence plots, error histogram analysis, error regression metrics, input-error cross-correlation, and error autocorrelation plots. Comparative analysis charts present the efficacious use of the DC-NARX intelligent computing paradigm with absolute errors ranging from 10-5 to 10-12. Predictive intelligence of the step ahead DC-NARX-BR strategy is observed for the intricate FHN model dynamics with marginal deviances from realized behavior. These diminutive errors can be comprehended by the low MSE losses in the range 10-2–10-5. Exhaustive experimentational averages validate the robustness of DC-NARX intelligent computing paradigm for the correct integration with the complex bioelectrical phenomena occurring within a neuronal cell membrane.