arXiv subjects

Daniel Tesfay

Publications and source records attributed to Daniel Tesfay.

8 recordsLinked to original sources

arXiv2026

Endogenous business cycles via state-dependent saving and noise-induced metastability

We develop a parsimonious stochastic growth model in which state-dependent saving behavior generates endogenous business-cycle-like dynamics. The model consists of three coupled equations: a Solow-type capital accumulation equation, a linear filtering equation for the saving rate, and a bounded stochastic adjustment process. Saving is modeled as a logistic function of deviations from a balanced growth path, introducing nonlinear feedback controlled by a gain parameter. In the deterministic limit, increasing feedback strength produces a supercritical pitchfork bifurcation, splitting the balanced-growth equilibrium into two locally attracting regimes corresponding to expansion and contraction. When stochastic perturbations are introduced, these equilibria become metastable states, and the economy undergoes rare noise-induced transitions between them. The resulting dynamics exhibit persistent regimes, bimodal stationary densities, and right-skewed dwell-time distributions with approximately exponential survival tails. A discrete-time approximation is estimated using U.S. real GDP data, and Monte Carlo simulations are used to compute stationary distributions and regime persistence statistics. The results demonstrate that nonlinear state dependence, bounded multiplicative noise, and time-scale separation are sufficient to generate realistic business-cycle behavior within a low-dimensional framework.

math.DS↗

arXiv2026

Stochastic bifurcation in economic growth model driven by L\'evy noise

This paper enhances the classical Solow model of economic growth by integrating L\'evy noise, a type of non-Gaussian stochastic perturbation, to capture the inherent uncertainties in economic systems. The extended model examines the impact of these random fluctuations on capital stock and output, revealing the role of jump-diffusion processes in long-term GDP fluctuations. Both continuous and discrete-time frameworks are analyzed to assess the implications for forecasting economic growth and understanding business cycles. The study compares deterministic and stochastic scenarios, providing insight into the stability of equilibrium points and the dynamics of economies subjected to random disturbances. Numerical simulations demonstrate how stochastic noise contributes to economic volatility, leading to abrupt shifts and bifurcations in growth trajectories. This research offers a comprehensive perspective on the influence of external shocks, presenting a more realistic depiction of economic development in uncertain environments.

econ.GN↗

arXiv2021

Dynamic Systems Framework for Modeling COVID-19 with L\'evy Noise

Natural fluctuations have played a crucial role in affecting the dynamics of pervasive diseases such as the coronavirus. Examining the effects of irregular unsettling disturbances on epidemic models is important for understanding these dynamics. In this study, we introduce a mathematical model for the SIR (Susceptible-Infectious-Recovered) dynamics of the coronavirus, incorporating perturbations in the contact rate through Levy noise. The utilization of the Levy process is essential for the protection and control of diseases. We delve into the dynamics of both the deterministic model and the global positive solution of the stochastic model, establishing their existence and uniqueness. Additionally, we explore conditions for the termination and persistence of the infection. Furthermore, we derive the basic reproduction number, a critical determinant of disease extinction or persistence. Numerical results indicate that COVID-19 dissipates from the population when the reproduction number is less than one in the presence of significant or minor noise. Conversely, controlling epidemic diseases becomes challenging when the reproduction number exceeds one. To illustrate this phenomenon, we provide numerical simulations, offering insights into the dynamics of the disease and the efficacy of control measures

math.DS↗

arXiv2021

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-diffusion Noise

We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Allee effect using the non-local Fokker-Planck equation. This stochastic model is driven by non-Gaussian as well as Gaussian noise, and it has three fixed points. One of them is the unstable state which lies between the two stable equilibria. We focus on the transition pathways from the extinction state to the upper fixed stable state for the transcription factor activator in a single-species model. This helps us to study the biological behavior of species. The most probable path is obtained from the solution of the non-local Fokker-Planck equation corresponding to the population system of the single-species model, and the corresponding maximum possible stable equilibrium state is determined. We also obtain the Onsager-Machlup (OM) function for the stochastic model and solve the corresponding most probable paths. The numerical simulation shows that: (i) When non-Gaussian noise is presented in the system, the maximum of the stationary density function is located at the most probable stable equilibrium state; (ii) If the initial value increases from extinction state to the upper stable state, the most probable trajectory goes to the maximal likely equilibrium state, in our case it lies between 9 and 10; (iii) The most probable paths increase to stable state quickly, then maintain a nearly constant level, and approach to the upper stable equilibrium state as time goes on. These numerical experiment findings accelerate growth for further experimental study, in order to achieve good knowledge about dynamical systems in biology.

math.DS↗

arXiv2020

Dynamics of a Stochastic COVID-19 Epidemic Model with Jump-Diffusion

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by $\xi$ which depends on the white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreaks as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that the COVID-19 vanishes from the population if $\xi <1;$ whereas the epidemic can't go out of control if $\xi >1.$ From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

q-bio.PE↗

arXiv2020

Stochastic Bifurcation in Single-Species Model Induced by {\alpha}-Stable Levy Noise

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic bifurcation techniques are infrequently employed. Here we establish stochastic P-bifurcation behavior of (i) a growth model with state-dependent birth rate and constant death rate, and (ii) a logistic growth model with state-dependent carrying capacity, both of which are driven by multiplicative symmetric stable Levy noise. Transcritical bifurcation occurs in the deterministic counterpart of the first model, while saddle-node bifurcation takes place in the logistic growth model. We focus on the impact of the variations of the growth rate, the per capita daily adult mortality rate, the stability index, and the noise intensity on the stationary probability density functions of the associated non-local Fokker-Planck equation. In the first model, the bifurcation parameter is the ratio of the population birth rate to the population death rate. In the second model, the bifurcation parameter corresponds to the sensitivity of carrying capacity to change in the size of the population near equilibrium. In each case, we show that as the value of the bifurcation parameter increases, the shape of the steady-state probability density function changes and that both stochastic models exhibit stochastic P-bifurcation. The unimodal density functions become more peaked around deterministic equilibrium points as the stability index increases. While an increase in any one of the other parameters has an effect on the stationary probability density function. That means the geometry of the density function changes from unimodal to flat, and its peak appears in the middle of the domain, which means a transition occurs.

math.DS↗

arXiv2020

A Logistic-Harvest Model with Allee Effect under Multiplicative Noise

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic differential equation driven by multiplicative Gaussian noise. With the help of the associated Fokker-Planck equation, we analyze the population extinction probability and the probability of reaching a large population size before reaching a small one. We further study the impact of the harvest rate, noise intensity, and the Allee effect on population evolution. The analysis and numerical experiments show that if the noise intensity and harvest rate are small, the population grows exponentially, and upon reaching the carrying capacity, the population size fluctuates around it. In the stochastic logistic-harvest model without the Allee effect, when noise intensity becomes small (or goes to zero), the stationary probability density becomes more acute and its maximum point approaches one. However, for large noise intensity and harvest rate, the population size fluctuates wildly and does not grow exponentially to the carrying capacity. So as far as biological meanings are concerned, we must catch at small values of noise intensity and harvest rate. Finally, we discuss the biological implications of our results.

q-bio.PE↗

arXiv2019

Transitions between Metastable States in a Simplified Model for the Thermohaline Circulation under Random Fluctuations

In this work, we study the impact of non-Gaussian alpha-stable Levy motion on transitions between metastable equilibrium states (or attractors) in a stochastic Stommel two-box model for thermohaline circulation (THC). By maximizing the probability density of the solution process associated with a nonlocal Fokker-Planck equation, we compute maximal likely pathways and identify corresponding maximal likely stable equilibrium states. Our numerical results indicate weakened THC may be induced by perturbation with very small noise intensity in a certain range of stability index. Moreover, larger noise intensity and larger stability index induce weakened THC within shorter bifurcation time.

physics.ao-ph↗