Search Results (44)

An investigation on a discrete-time infectious disease model that incorporating vertical transmission is presented in this paper. Departing from prior research centered on continuous-time frameworks, our study adopts a discrete-time formulation to better capture the complex epidemiological dynamics. We establish a model and conduct a bifurcation analysis of its equilibrium points. In particular, sufficient conditions for the local stability and the emergence of Neimark–Sacker and flip bifurcations are rigorously derived and analytically verified. As anticipated, variations in the bifurcation parameter give rise to distinct periodic regimes in the system response. To mitigate the instabilities and chaotic behaviors resulting from these bifurcations, we propose and validate two control strategies, which are Hybrid Control Method and State Feedback Control. Numerical simulations futher substantiated the analytical results, demonstrating that appropriate parameter adjustments can shift the system behavior from chaotic attractors and limit cycles toward stable equilibria. Our results show that by dynamically adjusting the intensity of prevention and control measures to mitigate unstable factors such as vertical transmission and high infection rates, or reducing the frequency of system updates to slow down the growth of infections, the epidemic can be transitioned from repeated outbreaks to a stable and manageable state. Full article

This study investigates the dynamic behavior of a discrete epidemic model as affected by media coverage through integrated analytical and numerical methods. The main objective is to quantitatively assess the impact of media coverage on disease outbreak models through mathematical modeling. We use the central manifold theorem and bifurcation theory to perform a rigorous analysis of the periodic solutions, focusing on the coefficients and conditions governing the flip bifurcation. On this basis, state feedback and hybrid control are utilized to control the system chaotically. Under certain conditions, the chaos and bifurcation of the system can be stabilized by the control strategy. Numerical simulations further reveal the bifurcation dynamics, chaotic behavior, and control techniques. Our results show that media coverage is a key factor in regulating the intensity and chaos of disease transmission. Control techniques can effectively prevent large-scale outbreaks of epidemics. Notably, enhanced media coverage can effectively increase public awareness and defensive behaviors, thus contributing to mitigating disease spread. Full article

This study examines a discrete-time predator–prey model constructed via piecewise constant discretization of its continuous counterpart. Through comprehensive qualitative and dynamical analyses, we reveal a rich set of nonlinear phenomena, encompassing Neimark–Sacker bifurcation, flip bifurcation, and codimension-two bifurcations corresponding to 1:2, 1:3, and 1:4 resonances. Rigorous analysis of these bifurcation scenarios, conducted via center manifold theory and bifurcation methods, establishes a robust mathematical framework for their characterization. Numerical simulations corroborate the theoretical predictions, exposing intricate dynamical phenomena such as quasiperiodic oscillations and chaotic attractors. Our results demonstrate that resonance-driven bifurcations are potent drivers of ecological complexity in discrete systems, acting as key determinants that orchestrate the emergent dynamics of populations—a finding with profound implications for interpreting patterns in real-world ecosystems subject to discrete generations or seasonal pulses. Full article

This study investigates the dynamic behaviors of the discrete epidemic model influenced by media coverage through integrated analytical and numerical approaches. The primary objective is to quantitatively assess the impact of media coverage on disease outbreak patterns using mathematical modeling. Firstly, the Euler method is used to discretize the model (2), and the periodic solution is strictly analyzed. Secondly, the coefficients and conditions of restricted flip and Neimark–Sacker bifurcation are studied by using the center manifold theorem and bifurcation theory. By calculating the largest Lyapunov exponent near the critical bifurcation point, the occurrence of chaos and limit cycles is proved. On this basis, the chaotic control of the system is carried out by using state feedback and hybrid control. Under certain conditions, the chaos and bifurcation of the system can be stabilized by control strategies. Numerical simulations further reveal bifurcation dynamics, chaotic behaviors, and control technologies. Our results show that media coverage is a key factor in regulating the intensity of disease transmission and chaos. The control technology can effectively prevent the large-scale outbreak of epidemic diseases. Importantly, enhanced media coverage can effectively promote public awareness and defensive behaviors, thereby contributing to the mitigation of disease transmission. Full article

We explore chaos, local dynamics, codimension-one, and codimension-two bifurcations of an asymmetric discrete predator–prey model. More precisely, for all the model’s parameters, it is proved that the model has two boundary fixed points and a trivial fixed point, and also under parametric conditions, it has an interior fixed point. We then constructed the linearized system at these fixed points. We explored the local behavior at equilibria by the linear stability theory. By the series of affine transformations, the center manifold theorem, and bifurcation theory, we investigated the detailed codimensions-one and two bifurcations at equilibria and examined that at boundary fixed points, no flip bifurcation exists. Furthermore, at the interior fixed point, it is proved that the discrete model exhibits codimension-one bifurcations like Neimark–Sacker and flip bifurcations, but fold bifurcation does not exist at this point. Next, for deeper understanding of the complex dynamics of the model, we also studied the codimension-two bifurcation at an interior fixed point and proved that the model exhibits the codimension-two 1:2, 1:3, and 1:4 strong resonances bifurcations. We then investigated the existence of chaos due to the appearance of codimension-one bifurcations like Neimark–Sacker and flip bifurcations by OGY and hybrid control strategies, respectively. The theoretical results are also interpreted biologically. Finally, theoretical findings are confirmed numerically. Full article

This study investigates dynamic behaviors within a competition Cournot duopoly framework incorporating consumer surplus, and social welfare through the bounded rationality method. The distinctive aspect of the competition game is the incorporation of discrete difference equations into the players’ optimization problems. Both rivals seek to achieve optimal quantity outcomes by maximizing their respective objective functions. The first firm seeks to enhance the average between consumer surplus and its profit, while the second firm focuses on its profit optimization with a social welfare component. The game map features four fixed points, with one being the Nash equilibrium point at the intersection of marginal objective functions. Our analysis explores equilibrium stability, dynamic complexities, basins of attraction, and the emergence of chaos through double routes via flip bifurcation and Neimark-Sacker bifurcations. We observe that increased adjustment speeds can destabilize the system, leading to a richness of dynamic complexity. Full article

Mismatched T:G base pairs can arise during de novo replication as well as base excision repair (BER). In particular, the action of the gap-filling polymerase β (Polβ) can generate a T:G pair as well as a nick in the DNA backbone. The processing of a nicked T:G mispair is poorly understood. We are interested in understanding whether the T:G-specific DNA glycosylase MBD4 can recognize and process nicked T:G mismatches. We have discovered that MBD4 binds a nicked T:G-containing DNA, but does not cleave thymine opposite guanine. To gain insight into this, we have determined a crystal structure of human MBD4 bound to a nicked T:G-containing DNA. This structure displayed the full insertion of thymine into the catalytic site and the recognition of thymine based on the catalytic site’s amino acid residues. However, thymine excision did not occur, presumably due to the inactivation of the catalytic D560 carboxylate nucleophile via a polar interaction with the 5′-hydrogen phosphate of the nicked DNA. The nicked complex was greatly stabilized by an ordered water molecule that formed four hydrogen bonds with the nicked DNA and MBD4. Interestingly, the arginine finger R468 did not engage in the phosphate pinching that is commonly observed in T:G mismatch recognition complex structures. Instead, the guanidinium moiety of R468 made bifurcated hydrogen bonding interactions with O6 of guanine, thereby stabilizing the estranged guanine. These observations suggest that R468 may sense and disrupt T:G pairs within the DNA duplex and stabilize the flipped-out thymine. The structure described here would be a close mimic of an intermediate in the base extrusion pathway induced by DNA glycosylase. Full article

This study addresses chaos control in a Buck–Boost converter using ZAD technique and FPIC. The system analysis identified 1-periodic orbits and observed the occurrence of flip bifurcations, indicating chaotic behavior characterized by sensitivity to initial conditions. To mitigate these instabilities, FPIC was successfully applied, stabilizing periodic orbits and significantly reducing chaos in the system. Numerical simulations verified the presence of chaos, confirmed by positive Lyapunov exponents, and demonstrated the effectiveness of the applied control methods. Steady-state and transient responses of the open-loop model and experimental system were evaluated, showing a strong correlation between them. Under varying load conditions, the numerical model accurately predicted the converter’s real dynamics, validating the proposed approach. Additionally, closed-loop control with ZAD exhibited robust performance, maintaining stable inductor current even during abrupt load changes, thus achieving effective control in non-minimum phase systems. This work contributes to the design of robust control strategies for power converters, optimizing their stability and dynamic response in applications that require precise management of power under variable conditions. Finally, a comparison was made between the performance of the Buck–Boost converter controlled with ZAD and the one controlled by PID. It was observed that both controllers effectively regulate the current, with a steady-state error of less than 1%. However, the system controlled with ZAD maintains a fixed switching frequency, whereas the PID-controlled system lacks a fixed switching frequency and operates with a very high PWM frequency. This high frequency in the PID-controlled system presents a disadvantage, as it leads to issues such as chattering, duty cycle saturation, and consequently, overheating of the MOSFET. Full article

This study theoretically investigates the impact of comb spacing irregularity on the dynamics of optically injected semiconductor lasers using a rate equation model. Bifurcation analysis, time-domain simulations, spectral properties, and Mode Suppression Ratio (MSR) calculations reveal that equal spacing induces strong mode competition and chaos, while unequal spacing suppresses chaos and enhances stability. Interestingly, the Flipped comb exhibits similar behavior to the unequal comb, further supporting the conclusion that relative spacing—not spectral order—governs stability the Arbitrary combs, though lacking structured spacing, demonstrate intermediate suppression, indicating that breaking uniformity mitigates instability, but optimal spacing maximizes stabilization. Extending beyond previous studies on frequency comb injection, this work identifies spacing irregularity as a key mechanism for chaos control, offering new strategies for laser stabilization in optical communications and photonic integration. Full article

The Basener and Ross mathematical model is widely recognized for its ability to characterize the interaction between the population dynamics and resource utilization of Easter Island. In this study, we develop and investigate a discrete-time version of the Basener and Ross model. First, the existence and the stability of fixed points for the present model are investigated. Next, we investigated various bifurcation scenarios by establishing criteria for the occurrence of different types of codimension-one bifurcations, including flip and Neimark–Sacker bifurcations. These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model’s complex dynamical structure. Numerical simulations are employed to validate and illustrate the theoretical predictions. Finally, through bifurcation diagrams, maximal Lyapunov exponents, and phase portraits, we uncover a diversity of dynamical characteristics, including limit cycles, periodic solutions, and chaotic attractors. Full article

Host–parasitoid systems are an essential area of research in ecology and evolutionary biology due to their widespread occurrence in nature and significant impact on species evolution, population dynamics, and ecosystem stability. In such systems, the host is the organism being attacked by the parasitoid, while the parasitoid depends on the host to complete its life cycle. This paper investigates the effect of parasitoid aggregation attacks on a host in a host–parasitoid model with self-diffusion on two-dimensional coupled map lattices. We assume that in the simulation of biological populations on a plane, the interactions between individuals follow periodic boundary conditions. The primary objective is to analyze the complex dynamics of the host–parasitoid interaction model induced by an aggregation effect and diffusion in a discrete setting. Using the aggregation coefficient k as the bifurcating parameter and applying central manifold and normal form analysis, it has been shown that the system is capable of Neimark–Sacker and flip bifurcations even without diffusion. Furthermore, with the influence of diffusion, the system exhibits pure Turing instability, Neimark–Sacker–Turing instability, and Flip–Turing instability. The numerical simulation section explores the path from bifurcation to chaos through calculations of the maximum Lyapunov exponent and the construction of a bifurcation diagram. The interconversion between different Turing instabilities is simulated by adjusting the timestep and self-diffusion coefficient values, which is based on pattern dynamics in ecological modeling. This contributes to a deeper understanding of the dynamic behaviors driven by aggregation effects in the host–parasitoid model. Full article

In this paper, we aim to solve the issue of pattern formation mechanisms in a spatiotemporally discrete activator–inhibitor model that incorporates self- and cross-diffusions. We seek to identify the conditions that lead to the emergence of complex patterns and to elucidate the principles governing the dynamic behaviors that result in these patterns. We first construct a corresponding coupled map lattice (CML) model based on the continuous activator–inhibitor reaction–diffusion system. In the reaction stage, we examine the existence, uniqueness, and stability of the homogeneous stationary state and specify the parametric conditions for realizing these properties. Furthermore, by applying the center manifold theorem, we perform a flip bifurcation analysis and confirm that the model is capable of undergoing flip bifurcation. In the diffusion stage, we focus on the analysis of Turing bifurcation and determine the parameter conditions for the emergence of Turing instability. Through numerical simulations, we validate and explain the results of our theoretical analysis. Our study reveals various Turing instability mechanisms by coupling Turing and flip bifurcations, which include pure-self-diffusion-Turing instability, pure-cross-diffusion-Turing instability, flip-self-diffusion-Turing instability, flip-cross-diffusion-Turing instability, and chaos-self-diffusion-Turing instability mechanisms. Under different mechanisms, we illustrate the corresponding Turing patterns and discover a rich variety of pattern types such as labyrinthine, mosaic, alternating mosaic, colorful mottled grid patterns with winding and twisted bands, and patterns with dense patches and twisted bands nested together. Our research provides a theoretical framework and numerical support for understanding the complex dynamical behaviors and pattern formations in activator–inhibitor models with self- and cross-diffusions. Full article

Defects in the free layer are considered to be the main cause of the balloon effect, but there is little insight into the synthetic antiferromagnetic (SAF) layer. To address this shortcoming, in this work, an optimized SAF layer was introduced in the perpendicular magnetic tunneling junction (pMTJ) stack to eliminate the low-probability bifurcated-switching phenomenon. The results indicated that the Hf field in the film stack improved significantly from ~5700 Oe to ~7500 Oe. A magnetoresistive random access memory (MRAM) test chip was also fabricated with a 300 mm process, resulting in a significantly improved ballooning effect. The results also indicated that the switching voltage decreased by 18.6% and the writing energy decreased by 33.7%. In addition, the low-probability stray field along the x-axis was thought to be the main cause of the ballooning effect, and was experimentally optimized for the first time by enhancing the SAF layer. This work provides a new perspective on spin-flipping dynamics, facilitating a deeper comprehension of the internal mechanism and helping to secure improvements in MRAM performance. Full article

This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model. Full article

This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin’s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic’s spread. Full article