Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure

Modelling and Analysis of a Pest-Control Pollution Model with Integrated Control Tactics

A hybrid impulsive pest control model with stage structure for pest and Holling II functional response is proposed and investigated, in which the effects of impulsive pesticide input in the environment and in the organism are considered. Sufficient conditions for global attractiveness of the pest-extinction periodic solution and permanence of the system are obtained, which show that there exists a globally asymptotically stable pest-extinction periodic solution when the number of natural enemies released is more than some critical value, whereas the system can be permanent when the number of natural enemies released is less than another critical value. Furthermore, numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation

Existence and stability of periodic solution of a Lotka–Volterra predator–prey model with state dependent impulsive effects

AbstractAccording to biological and chemical control strategy for pest, we investigate the dynamic behavior of a Lotka–Volterra predator–prey state-dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds. By using Poincaré map and the properties of the Lambert W function, we prove that the sufficient conditions for the existence and stability of semi-trivial solution and positive periodic solution. Numerical simulations are carried out to illustrate the feasibility of our main results

Mathematical and Dynamic Analysis of a Prey-Predator Model in the Presence of Alternative Prey with Impulsive State Feedback Control

The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results

I want it now so you cannot have it later: The role of impulsive choices in competitive environments

Doctor of PhilosophyDepartment of Psychological SciencesMichael YoungPeople commonly prefer smaller-sooner rewards over larger-later rewards, referred to as impulsive choice. Although impulsive choices are strongly associated with negative behaviors, such as poor diet and exercise habits, substance abuse and gambling, larger delayed rewards are more uncertain than smaller immediate rewards regarding if and when they are delivered. The threat of losing out on delayed rewards may then motivate individuals to shift their preferences towards more immediately available goals. One source of uncertainty for delayed rewards is competition, where multiple individuals exclusively pursue limited resources. The impact of competitors may result in individuals selecting more impulsive choices to ensure a relatively greater acquisition of important resources compared to competitors, despite the environment originally incentivizing waiting. Therefore, the purpose of the current dissertation is to study the degree to which competition-based uncertainty increases impulsive choices above and beyond environmental uncertainty. To test this hypothesis, I conducted two experience-based decision-making experiments that manipulated various dimensions of competition that could potentially control participants’ waiting behaviors and performance, such as the visibility of a competitor and the visibility of the competitor’s cumulative rewards. Overall, the results provided weak evidence that competition influenced participants’ impulsive choices above environmental uncertainty, specifically by slightly increasing their likelihood of obtaining rewards rather than their tendency to select impulsive choices. These findings are more consistent with an economic perspective of choice behavior than an evolutionary perspective, and I discuss the theoretical and methodological implications of this novel line of research

The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Furthermore,when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results