Discrete-time Model Research Articles

A discrete-time dynamical model of prey and stage-structured predator with juvenile hunting incorporating negative effects of prey refuge

This paper examines a discrete predator–prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting along with its negative effects in the form of prey counterattack is considered. This paper provides a comprehensive analysis of the existence and stability conditions pertaining to all possible fixed points of this system. The impact of the parameters reflecting prey growth and prey refuge is thoroughly discussed. This paper delves into the occurrence of the Neimark–Sacker bifurcation and period-doubling bifurcation, specifically in relation to the parameters associated with prey growth rate and prey refuge. Numerous numerical simulations are presented in order to validate the theoretical findings.

New discrete-time zeroing neural network for solving time-dependent linear equation with boundary constraint

Recently, continuous- and discrete-time models of a zeroing neural network (ZNN) have been developed to provide online solutions for the time-dependent linear equation (TDLE) with boundary constraint. This paper presents a novel approach to address the bound-constrained TDLE (BCTDLE) problem by proposing a new discrete-time ZNN (DTZNN) model. The proposed DTZNN model is designed using the Taylor difference formula to discretize the previous continuous-time ZNNN (CTZNN) model. Theoretical analysis indicates the computational property of the proposed DTZNN model, and numerical results further demonstrate its validity. The applicability of the proposed DTZNN model is finally confirmed via its application to the motion planning of a PUMA560 robotic arm.

Evaluating the influence of taxation and social security policies on psychological distress: A microsimulation study of the UK during the COVID-19 economic crisis

Economic determinants are important for population health, but actionable evidence of how policies can utilise these pathways remains scarce. This study employs a microsimulation framework to evaluate the effects of taxation and social security policies on population mental health. The UK economic crisis caused by the COVID-19 pandemic provides an informative context involving an economic shock accompanied by one of the strongest discretionary fiscal responses amongst OECD countries.The analytical setup involves a dynamic, stochastic, discrete-time microsimulation model (SimPaths) projecting changes in psychological distress given predicted economic outcomes from a static tax-benefit microsimulation model (UKMOD) based on different policy scenarios. We contrast projections of psychological distress for the working-age population from 2017 to 2025 given the observed policy environment against a counterfactual scenario where pre-crisis policies remained in place. Levels of psychological distress and potential cases of common mental disorders (CMDs) were assessed with the 12-item General Health Questionnaire (GHQ-12).The UK policy response to the economic crisis is estimated to have prevented a substantial fall (over 12 percentage points, %pt) in the employment rate in 2020 and 2021. In 2020, projected psychological distress increased substantially (CMD prevalence increase >10%pt) under both the observed and the counterfactual policy scenarios. Through economic pathways, the policy response is estimated to have prevented a further 3.4%pt [95%UI 2.8%pt, 4.0%pt] increase in the prevalence of CMDs, approximately 1.2 million cases. Beyond 2021, as employment levels rapidly recovered, psychological distress returned to the pre-pandemic trend. Sustained preventative effects on poverty are estimated, with projected levels 2.1%pt [95%UI 1.8%pt, 2.5%pt] lower in 2025 than in the absence of the observed policy response.The study shows that policies protecting employment during an economic crisis are effective in preventing short-term mental health losses and have lasting effects on poverty levels. This preventative effect has substantial public health benefits.

Discrete-Time Adaptive Control for Three-Phase PWM Rectifier.

This paper proposes a dual-loop discrete-time adaptive control (DDAC) method for three-phase PWM rectifiers, which considers inductance-parameter-mismatched and DC load disturbances. A discrete-time model of the three-phase PWM rectifier is established using the forward Euler discretization method, and a dual-loop discrete-time feedback linearization control (DDFLC) is given. Based on the DDFLC, the DDAC is designed. Firstly, an adaptive inductance disturbance observer (AIDO) based on the gradient descent method is proposed in the current control loop. The AIDO is used to estimate lump disturbances caused by mismatched inductance parameters and then compensate for these disturbances in the current controller, ensuring its strong robustness to inductance parameters. Secondly, a load parameter adaptive law (LPAL) based on the discrete-time Lyapunov theory is proposed for the voltage control loop. The LPAL estimates the DC load parameter in real time and subsequently adjusts it in the voltage controller, achieving DC load adaptability. Finally, simulation and experimental results show that the DDAC exhibits better steady and dynamic performances, less current harmonic content than the DDFLC and the dual-loop discrete-time PI control (DDPIC), and a stronger robustness to inductance parameters and DC load disturbances.

One way or another: Combined effect of dispersal and asymmetry on total realized asymptotic population abundance

Understanding the consequences on population dynamics of the variability in dispersal over a fragmented habitat remains a major focus of ecological and environmental inquiry. Dispersal is often asymmetric: wind, marine currents, rivers, or human activities produce a preferential direction of dispersal between connected patches. Here, we study how this asymmetry affects population dynamics by considering a discrete-time two-patch model with asymmetric dispersal. We conduct a rigorous analysis of the model and describe all the possible response scenarios of the total realized asymptotic population abundance to a change in the dispersal rate for a fixed symmetry level. In addition, we discuss which of these scenarios can be achieved just by restricting mobility in one specific direction. Moreover, we also report that changing the order of events does not alter the population dynamics in our model, contrary to other situations discussed in the literature.

Analyses of the SIR Epidemic Model Including Treatment and Immigration

This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete-time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points in the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of flip bifurcation. A feedback control strategy is applied to control the chaos occurring in the system after a certain period of time. We also perform numerical simulations to support analytical results. We do all these analyses for models with and without immigration and show the effect of immigration on dynamics.

A dynamic channel aggregation strategy with a maximum aggregation number in cognitive radio networks based on channel classification

In traditional cognitive radio networks (CRNs), users are generally divided into two categories: primary users (PUs) and secondary users (SUs). The transmission rates of different channels may vary due to the complexities of network transmissions. Therefore, in this paper, a channel classification mechanism that divides the channels in the system into high-speed channels and low-speed channels according to their transmission capacity is proposed. In addition, to improve the performance of users, a dynamic channel aggregation strategy for CRNs with two types of channels is proposed. In this strategy, packets first consider accessing high-speed channels. We set a fixed channel aggregation strategy for PU packets and a dynamic channel aggregation strategy for SU packets. The number of channel aggregation of SU packets is restricted by the maximum aggregation number. Based on the proposed strategy, a multi-service discrete-time queueing model is established and analyzed, and the performance index expressions of PU packets and SU packets are derived. Moreover, we conduct numerical experiments, obtain the system performance figures and analyze the system performance. Finally, the performance of the proposed channel aggregation strategy is compared with that of the non-aggregation strategy, verifying the effectiveness of the proposed channel aggregation strategy.

Qualitative analysis of solutions for a degenerate partial differential equations model of epidemic spread dynamics

Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations.

Dynamics and control of a plant-herbivore model incorporating Allee's effect

This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect. We specifically investigate a model that incorporates a strong predator functional response to better understand the system's qualitative behavior at positive equilibrium points. In the present study, we explore the topological classifications at fixed points, stability analysis, Neimark-Sacker, Transcritical bifurcation and State feedback control in the two-dimensional discrete-time plant-herbivore model. It is proved that for all involved parameters ς1,ϱ1,γ1 and ϒ1, discrete-time plant-herbivore model has boundary and interior fixed points: c1=(0,0), c2=(ς1−1ϱ1,0) and c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1) respectively. Then by linear stability theory, local dynamics with different topological classifications are investigated at fixed points: c1=(0,0), c2=(ς1−1ϱ1,0) and c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1). Our investigation uncovers that the boundary equilibrium c2=(ς1−1ϱ1,0) experiences a transcritical bifurcation, whereas the unique positive steady-state c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1) of the discrete-time plant-herbivore model undergoes a Neimark-Sacker bifurcation. To address the periodic fluctuations in grapevine population density and other unpredictable behaviors observed in the model, we propose implementing state feedback chaos control. To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent. These visual representations enhance the clarity of our research outcomes and further validate the effectiveness of the chaos control approach.

Lifetime prevalence, risk, and treatment of mood and anxiety disorders in Qatar's national mental health study.

To estimate lifetime prevalence, risk, and treatment for mental disorders and their correlates in Qatar's general population for the first time. We conducted a national phone survey of 5,195 Qatari and Arab residents in Qatar (2019-2022) using the Composite International Diagnostic Interview Version 3.3 and estimated lifetime mood and anxiety defined diagnoses. Survival-based discrete time models, lifetime morbid risk, and treatment projections were estimated. Lifetime prevalence of any disorder was 28.0% and was associated with younger cohorts, females, and migrants, but lower formal education. Treatment contact in the year of disorder onset were 13.5%. The median delay in receiving treatment was 5years (IQR=2-13). Lifetime treatment among those with a lifetime disorder were 59.9% for non-healthcare and 63.5% for healthcare; it was 68.1% for any anxiety and 80.1% for any mood disorder after 50years of onset.Younger cohorts and later age of onset were significantly predictors of treatment. Lifetime prevalence of mental disorders in Qatar is comparable to other countries. Treatment is significantly delayed and delivered largely in non-healthcare sectors thus the need for increased literacy of mental illness to reduce stigma and improve earlier help-seeking in healthcare settings.

(r, Q) stock replenishment in multi-mode distribution systems with uncertain delivery channels and adaptive channel allocation

To mitigate the impact of uncertainty in goods distribution systems, multiple channels and transportation modes may be used. In this paper, a discrete-time model of supplier-depot interaction involving multiple channels of goods relocation is constructed using the concepts of dynamic systems theory. The considered class of systems faces two types of uncertainty: a priori unknown variations of market demand and unpredictable changes of lead-time delay, different for each channel. The variation pattern is arbitrary. As a control mechanism, the nonlinear (r, Q) replenishment policy (provide Q units of goods when the stock falls below r) is considered. As opposed to the previous studies, the policy is demonstrated robust to both sources of uncertainty acting simultaneously using a formal mathematical argument. Moreover, it is shown how to select the policy parameters to obtain full demand realization, thus eliminating backorders, irrespective of the pattern of delay and demand fluctuations. It is also discussed how to assign the depot capacity so that emergency storage will not be required even though deliveries from a few periods arrive concurrently, or out of order. In addition, a new channel allocation strategy, dynamically adapting itself to the channel temporal characteristics, is developed. As evidenced in the tests, the proposed adaptive strategy, by reducing the waiting time for the lot reassembly at the depot, allows for holding cost reduction by several percent with respect to a static strategy.

Mean-squared exponential stability of distributed almost periodic sequence for nonlocal space-time discrete shunting inhibitory cellular neural networks with Brownian motions

The discrete-time and discrete-space model for stochastic nonlocal shunting inhibitory cellular neural networks with reaction diffusions are modelled in the first time. Owing to the consideration of spatial variables, the discrete model derived in this article is more complex than the traditional ordinary difference model. In accordance with the constant-variation-formula for discrete-time and discrete-space model, Banach contracting mapping principle, the method of proof by contradiction and stochastic calculus, we also obtain the existence of a unique bounded almost periodic sequence for the discrete model, which is exponentially stable in the mean-square sense. Noting that it is the first time to consider the dynamics of almost periodicity in distribution of time-space discrete neural network models. The practicability of the present results is demonstrated by means of an illustration.

The Intergenerational Transmission of Health Disadvantage: Can Education Disrupt It?

In low-income countries, intergenerational processes can culminate in the replication of extreme forms of health disadvantage between mothers and adult daughters, including experiencing a young child's death. The preventable nature of most child deaths raises questions of whether social resources can protect women from enduring this adversity like their mothers. This study examined whether education-widely touted as a vehicle for social mobility in resource-poor countries-disrupts the intergenerational cycle of maternal bereavement. We estimated multilevel discrete-time survival models of women's hazard of child loss using Demographic and Health Survey Program data (N = 195,744 women in 345 subnational regions in 32 African countries). Women's educational attainment minimizes the salience of their mothers' bereavement history for their own probability of child loss; however, mothers' background becomes irrelevant only among women with ≥10 years of schooling. Education's neutralizing influence is most prominent in the highest mortality-burdened communities.

A discrete-time model of phenotypic evolution

A model is proposed for the phenotypic evolution of a very large population under sustained environmental change and non-overlapping generations, with a single trait considered. Due to an extension of the standard law of quantitative inheritance, each evolutionary mechanism corresponds to a function between random variables associated with distinct stages of the life cycle. Such an approach leads to a two-dimensional map where the dynamics of the phenotypic mean and variance are directly connected. Then, the declining population paradigm is explored in terms of the critical rate of environmental change and using the techniques of the dynamical systems theory. Our results first reveal the opposing pressures on the phenotypic variance due to the conflict between phenotypic load and the ability to pursue the optimum, translated into an optimal value for maximizing the critical rate. Secondly, the introduction of development, through the particular case of linear plasticity, leads to a decreasing degree of stability with the magnitude of plasticity, which means that the recovery time from disturbances is harmed as the plastic effect intensifies, even though no constitutive costs have been assumed, a feature almost as important as the mean fitness to the viability of populations subject to persistent changes. Notwithstanding, the system is stable, and the growth rate benefits from increased plasticity, as expected.

Quasi-Projective Synchronization of Discrete-Time Fractional-Order Complex-Valued BAM Fuzzy Neural Networks via Quantized Control

In this paper, we ponder a kind of discrete-time fractional-order complex-valued fuzzy BAM neural network. Firstly, in order to guarantee the quasi-projective synchronization of the considered networks, an original quantitative control strategy is designed. Next, by virtue of the relevant definitions and properties of the Mittag-Leffler function, we propose a novel discrete-time fractional-order Halanay inequality, which is more efficient for disposing of the discrete-time fractional-order models with time delays. Then, based on the new lemma, fractional-order h-difference theory, and comparison principle, we obtain some easy-to-verify synchronization criteria in terms of algebraic inequalities. Finally, numerical simulations are provided to check the accuracy of the proposed theoretical results.

The impact of bank loans on university student retention

PurposeThis study analyzed the impact on the persistence of Chilean university students who had received a government-guaranteed loan (CAE).Design/methodology/approachUsing academic and administrative data from 2016 to 2019, provided by 11 Chilean universities, a discrete-time survival model was constructed. The model was based on data of 5,276 students in the 2016 cohort and included sociodemographic variables, academic background prior to entering university and academic performance once in university. As a robustness check of our results to observable confounding, the analysis was repeated using a control group constructed using propensity score matching (PSM).FindingsThe results reveal that students who receive a bank loan (CAE) were more likely to remain in undergraduate studies for at least the first two years of university, as opposed to their peers who did not receive financial aid. In addition, they show the importance of academic performance in retention.Originality/valueThe article advances in the identification of the impact of bank loans on permanence. Although previous research has evaluated the impact of the CAE, it has been conducted on small samples of students. These studies also lacked student records associated with their academic performance at the university. The present research overcomes both weaknesses, allowing us to estimate the impact of the CAE on a larger population of students that is representative of the system.

The chemostat reactor: A stability analysis and model predictive control

This contribution develops the model predictive control for an unstable chemostat reactor. Initially, we analyze the system’s model — a nonlinear first-order hyperbolic partial integro-differential equation (PIDE) — and carry the model linearization around an unstable operating condition. Employing the structure-preserving Cayley–Tustin transformation, we obtain a discrete-time model representation of the continuous model. Subsequently, we solve the operator Ricatti equations in the discrete-time setting to derive a full state feedback controller that stabilizes the closed-loop and design a Luenberger observer for state reconstruction given the system output measures. Finally, we formulate a dual-mode MPC ensuring constraint satisfaction and optimality, integrating the gain-based unconstrained full-state feedback optimal control obtained from the Ricatti equation. This dual-mode strategy describes an optimization problem where the predictive controller acts only if constraints become active within the control horizon. Simulation studies validate the controller performance, where the MPC only takes action if the constraints are predicted to be active within the control horizon while also guaranteeing closed-loop stabilization under only output feedback. This type of controller can be easily implemented with other control strategies and significantly decreases the computational costs of solving the optimal control problems when compared to other MPC approaches.

Leader-Following Formation Control for Discrete-Time Fractional Stochastic Multi-Agent Systems by Event-Triggered Strategy

Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for pinning control. In order to save resources and energy, an event-triggered based control mechanism is proposed. Second, under this control mechanism, sufficient conditions on the interaction graph and the fractional derivative order such that formation control can be achieved are given. Additionally, influenced by noise, the multi-agent system completes formation control in the mean square. In addition to that, these results are equally applicable to the discrete-time fractional formation problem without noise. Finally, the example of numerical simulation is given to prove the correctness of the results.

Chaotic dynamics of a three-species food chain model

An analysis of a discrete-time food chain model is presented in this paper to investigate the effects of strong prey pressure on the chain. A bifurcation and stability theory is used to analyze equilibrium formation in system. It is shown by numerical simulations that chaos occurs as a result of the bifurcation of invariant curves following Neimark-Sacker (NS) bifurcation rules. The OGY method on stable periodic orbits of period 1 further controls chaos. Stability is achieved through iterations for chaotic motion controlled by different regulator poles. Numerical simulations are performed to examine the effects of the control method along with the results of our theoretical analysis.

Cross-substance Effects of Adolescent Exposure to Alcohol Content in Popular Movies on Cannabis Initiation.

Alcohol is the most frequently depicted substance in the media, and adolescent exposure to alcohol in the media predicts alcohol use. There is relatively little research on exposure to cannabis in the media, but exposure to alcohol content may exert cross-substance effects on cannabis use. Given the social and health risks associated with early cannabis use, the present study aims to assess the cross-substance effects of exposure to alcohol media content on age of cannabis initiation. A sample of 830 middle school students (53% female) reported on movie alcohol exposure and cannabis initiation longitudinally until high school completion. Discrete-time survival models examined whether movie alcohol exposure predicted subsequent initiation among students who were cannabis-naïve at baseline, controlling for demographic, social, and behavioral covariates. The interaction between sex and movie alcohol exposure was also explored. One third (33%) of participants reported cannabis initiation with a mean of 5.57 estimated hours (SD = 4.29) of movie alcohol exposure. A 1-hour increase in movie exposure predicted a significant 16% increased probability of cannabis initiation in models adjusted for demographic variables and a significant 14% increase in models adjusted for demographic, behavioral, and social variables. No differences were observed across sex. Greater adolescent exposure to alcohol content in the media was associated with earlier cannabis initiation above and beyond other etiologically relevant demographic, behavioral, and social variables. The influence of cross-substance media exposures warrants further exploration and should be taken into consideration in the development of preventive interventions for youth substance use.