A delay-dividing approach to robust stability of uncertain stochastic complex-valued Hopfield delayed neural networks

In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model

Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature

Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Itoˆ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results

Visualization and Interpretation of PM10 Monitoring Data Related to Causes of Haze Episodes in Northern Thailand

Monitoring of ambient air quality yields data typically presented as time series plots, tables of summarized statistical values, or other representations. This paper presents an alternative way to visualizing air quality monitoring data by presenting concentrations in the form of a calendar, offering a familiar way for reader to identify air quality trends on various time scales (daily, weekly, or monthly). One of the major air pollution problems in the northern part of Thailand is haze, which is related to the concentration of airborne particulates less than 10 microns in size (PM10). This paper presents calendars of PM10 concentrations monitored by the Pollution Control Department across northern Thailand. Hourly mean PM10 concentrations monitored at 13 stations were used to construct PM10 concentration calendars for each station. Haze episodes are clearly identifiable in the visualization; the calendar also allows easy comparison of PM10 levels between years. We also observed the absence of any haze episodes in 2011, and propose possible related factors.

Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results

Regional Observed Trends in Daily Rainfall Indices of Extremes over the Indochina Peninsula from 1960 to 2007

This study analyzed the trends of extreme daily rainfall indices over the Indochina Peninsula from 1960 to 2007. The trends were obtained from high-resolution gridded daily rainfall data compiled by APHRODITE with coordinates of 4°N–25°N and 90E°–112°E. The indices were selected from the list of climate change indices recommended by ETCCDI, which is a joint group of WMO CCl, CLIVAR and JCOMM. The indices are based on the number of heavy rainfall days (≥10 mm), number of very heavy rainfall days (≥20 mm), number of extremely heavy rainfall days (≥25 mm), consecutive dry days (<1 mm), consecutive wet days (≥1 mm), daily maximum rainfall, five-day maximum rainfall, annual wet-day rainfall total, Simple Daily Intensity Index, very wet days, and extremely wet days. The indices were simulated by calculating different extreme characteristics according to wet and dry conditions, frequency, and intensity. Linear trends were calculated by using a least squares fit and significant or non-significant trends were identified using the Mann–Kendall test. The results of this study revealed contrasting trends in extreme rainfall in eastern and western Indochina Peninsula. The changes in extreme rainfall events in the east primarily indicate positive trends in the number of heavy rainfall days, very heavy rainfall days, extremely heavy rainfall days, consecutive wet days and annual wet-day rainfall total, with significant trends at times. These events correlated with the northeastern monsoon that influences the Indochina Peninsula from October to February annually. The results in the west primarily indicate negative trends in consecutive wet days, where significant trends were correlated with decreasing number of annual wet-day rainfall total, heavy rainfall days, very heavy rainfall days, and extremely heavy rainfall days. Daily maximum rainfall, five-day maximum rainfall, very wet days, and extremely wet days show random positive (negative) significant (non-significant) trends, while the simple daily intensity index shows positive trends that dominate the southern part of the Indochina Peninsula, with some grids show significant trends

Simulation of Marine Debris Path Using Mathematical Model in the Gulf of Thailand

Marine debris is an important environmental problem that affects aquatic animals, ecosystems, economy, society, and humans. This research aims to simulate the path of marine debris in the Gulf of Thailand using a mathematical model that includes two models: the Oceanic Model (OCM), which is based on the Shallow Water Equations (SWE), and the Lagrangian Particle Tracking (LPT) model. The OCM is the partial derivative equation system solved by the finite difference method to satisfy the Arakawa C-grid and the splitting method. The LPT model includes the current velocity, wind velocity at 10 m above sea level, random walk term, and the buoyancy ratio of marine debris with six cases, which are 100:1, 10:1, 1:1, 0:1, 1:10, and 1:100. The current velocity from OCM is applied to the LPT model. This research uses a garbage boat that capsized near Koh Samui on 1 August 2020 as a case study. The simulated current velocity of OCM is compared with Ocean Surface Current Analyses Real-time (OSCAR) data. The Root Mean Square Error (RMSE) of u-velocity is 0.070 m/s, and that of v-velocity is 0.058 m/s. The simulation of the marine debris’s path from the LPT model demonstrates the movement to Koh Samui, Koh Taen, Koh Wang Nai, Koh Wang Nok, Koh Rap, the east coast of Nakorn Si Thammarat province, Phu Quoc Island of Vietnam and the middle of the Gulf of Thailand with the different buoyancy ratios and time durations

The SQEIRP Mathematical Model for the COVID-19 Epidemic in Thailand

The spread of COVID-19 started in late December 2019 and is still ongoing. Many countries around the world have faced an outbreak of COVID-19, including Thailand, which must keep an eye on the spread and find a way to deal with this extreme outbreak. Of course, we are unable to determine the number of people who will contract this disease in the future. Therefore, if there is a tool that helps to predict the outbreak and the number of people infected, it will be able to find preventive measures in time. This paper aims to develop a mathematical model suitable for the lifestyle of the Thai population facing the COVID-19 situation. It has been established that after close contact with an infected person, a group of individuals will be quarantined and non-quarantined. If they contract COVID-19, they will enter the incubation period of the infection. The incubation period is divided into the quarantine class and the exposed class. Afterwards, both classes will move to the hospitalized infected class and the infected class, wherein the infected class is able to spread the disease to the surrounding environment. This study describes both classes in the SQEIRP model based on the population segmentation that was previously discussed. After that, the positive and bounded solutions of the model are examined, and we consider the equilibrium point, as well as the global stability of the disease-free point according to the Castillo-Chavez method. The SQEIRP model is then numerically analyzed using MATLAB software version R2022a. The cumulative percentage of hospitalized and non-hospitalized infections after 7 days after the commencement of the infection was determined to be 11 and 34 percent of the entire population, respectively. The Next-Generation Matrix approach was used to calculate the Basic Reproduction Numbers (R0). The SQEIRP model’s R0 was 3.78, indicating that one infected individual can result in approximately three additional infections. The results of this SQEIRP model provide a preliminary guide to identifying trends in population dynamics in each class

Mathematical Model for Rice Blast Disease Caused by Spore Dispersion Affected from Climate Factors

Rice blast disease, caused by the fungus Pyricularia oryzae, is one of the diseases that reduce rice yields in Thailand. The fungus’s dispersal influences this disease outbreak. This study aims to develop a mathematical model for spore dispersion, namely a non-local diffusion equation in terms of the dispersal kernel, by adding a factor that causes spore dispersion due to rain splash and adjusting the infection term based on weather conditions such as air temperature and relative humidity. The model assessed the existence and uniqueness of solutions by Banach’s fixed point theorem and used a finite difference method to solve them. The numerical simulation confirmed the existence and uniqueness part of the analysis. Because the climate data was used effectively for developing the disease, the rice blast disease pandemic was widespread in the study areas

Spatio-Temporal Variability of Winter Monsoon over the Indochina Peninsula

In this study, the spatial patterns and their interannual variability of wintertime low-level winds over the Indochina Peninsula (IDP) were studied by using the analysis of the empirical orthogonal function for complex numbers. The leading mode accounts for 46.6% of the total variance. The composite and regressed patterns of wind components show dominant northeasterly wind over the IDP, which are related to the East Asia winter monsoon (EAWM) circulation and connected to the cyclonic circulation near Borneo. The correlations between the EAWM indices and the leading principal component (PC) suggest the plausible connections between the low-level wind over the IDP and EAWM predominantly via the wind circulation. We also performed correlation analysis on the relationship between leading mode and sea surface temperature anomalies (SSTAs). The result indicates that there is a linkage between the northeasterly wind over the IDP and EAWM and with SSTAs in the Pacific Ocean. This study provides useful information and a mechanism related to the monsoon variability over the IDP