Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III

Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.

Stability Analysis and Harvesting Effort Predator Prey Populations Model Holling Type III with Maximum Profit

In this paper discussed stability analysis and harvesting effort at second predator prey populations model Holling type III with maximum profit. The step this research is to determine the equilibrium point, linearize the model, stability analysis of the equilibrium point, and numerical simulation. Result shows that obtained an interior point T𝐸2∗(𝑁1∗,𝑁2∗) that asymptotic stable based on Hurwitz stability test then obtained maximum profit from exploitation harvesting effort of second predator prey populations. This second populations will always exist, even though exploited with harvesting effort done by humans. Harvesting effort of second predator-prey populations given maximum profit (𝜋𝑚𝑎𝑥) that occur on critical points of surface profit function

Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the Susceptible-Infectious-Recovered (SIR)-type epidemiological model that we developed for viral diseases with long-term immunity memory. This is a large-scale model containing 15 nonlinear ordinary differential equations (ODEs), and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions thanks to the symmetry of the population size over time.

Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-type Epidemiological Models

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the SIR-type epidemiological model that we developed for viral diseases with long-term immunity memory pandemic. This is a large-scale model containing 15 nonlinear ODE equations, and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions.

Robust backstepping attitude tracking control of an underactuated spacecraft with saturation and time-variant perturbations

This study investigated associations of attitude tracking control of an underactuated spacecraft with consideration of saturation and perturbations. A nonsingular attitude tracking control was proposed which did not need limiting initial conditions of the quaternions. The controller was analyzed based on Lyapunov criteria and LaSalle’s invariance theorem in the large-angle maneuver. In order to control, the complete kinematic and dynamic model of the underactuated spacecraft was reconstructed. According to simulation results, our controller has excellent robustness against the hard saturation, external disturbances, time-varying inertia uncertainties, and internal disturbances of actuators. As result, we found that the attitude controller was asymptotically stable under the soft saturation and the perturbations so that quaternions and angular velocity converged to the desired path within the 80 s. Also, it was still asymptotic stable under the hard saturation whose level is equal to 0.035 Nm, 3.5% of the soft saturation level. In this case, errors of quaternions and angular velocity were converged to the origin within the 150 s. Finally, the closed-loop system was verified by Adams-MATLAB co-simulation. The maximum verification errors for quaternions were less than 19%, while the maximum verification errors for angular velocity were less than 13.5%.

Asymptotic Behavior by Krasnoselskii Fixed Point Theorem for Nonlinear Neutral Differential Equations with Variable Delays

In this paper, we consider a neutral differential equation with two variable delays. We construct new conditions guaranteeing the trivial solution of this neutral differential equation is asymptotic stable. The technique of the proof based on the use of Krasnoselskii’s fixed point Theorem. An asymptotic stability theorem with a necessary and sufficient condition is proved. In particular, this paper improves important and interesting works by Jin and Luo. Moreover, as an application, we also exhibit some special cases of the equation, which have been studied extensively in the literature.

Bistable and oscillatory dynamics of Nicholson's blowflies equation with Allee effect

<p style='text-indent:20px;'>The bistable dynamics of a modified Nicholson's blowflies delay differential equation with Allee effect is analyzed. The stability and basins of attraction of multiple equilibria are studied by using Lyapunov-LaSalle invariance principle. The existence of multiple periodic solutions are shown using local and global Hopf bifurcations near positive equilibria, and these solutions generate long transient oscillatory patterns and asymptotic stable oscillatory patterns.</p>

A study on COVID-19 transmission dynamics: Stability analysis of SEIR model with Hopf bifurcation for effect of time delay

This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter $\tau$ is the effects of time delay and we demonstrate that the locally asymptotic stable is present equilibrium. The Reproduction number is brief in less than or greater than one, and it effectively controlling the COVID-19 infection outbreak, and subsequently reveals insight into understanding the patterns of the flare-up. The numerical experiment is calculated to help the theoretical outcomes.

Nonlinear Dynamics, Switching Kinetics and Physical Realization of the Family of Chua Corsage Memristors

This article reviews the nonlinear dynamical attributes, switching kinetics, bifurcation analysis, and physical realization of a family of generic memristors, namely, Chua corsage memristors (CCM). CCM family contains three 1-st order generic memristor dubbed as 2-lobe, 4-lobe, and 6-lobe Chua corsage memristors and can be distinguished in accordance with their asymptotic stable states. The 2-lobe CCM has two asymptotically stable equilibrium states and regarded as a binary memory device. In contrast, the versatile 4-lobe CCM and 6-lobe CCM are regarded as a multi-bit-per-cell memory device as they exhibit three and four asymptotic stable states, respectively, on their complex and diversified dynamic routes. Due to the diversified dynamic routes, the CC memristors exhibit a highly nonlinear DC V-I curve. Unlike most published highly-nonlinear DC V-I curves with several disconnected branches, the DC V-I curves of CCMs are contiguous along with a locally active negative slope region. Moreover, the DC V-I curves and parametric representations of the CCMs are explicitly analytical. Switching kinetics of the CCM family can be demonstrated with universal formulas of exponential state trajectories xn(t), time period tfn, and applied minimum pulse amplitude VA and width Δw. These formulas are regarded universal as they can be applied to any piecewise linear dynamic routes for any DC or pulse input and with any number of segments. When local activity, and bifurcation and chaos theorems are employed, CMMs exhibit unique stable limit cycles spawn from a supercritical Hopf bifurcation along with static attractors. In addition, the nonlinear circuit and system theoretic approach is applied to explain the asymptotic stability behavior of CCMs and to design real memristor emulators using off-the-shelf circuit components.