This paper studies the autonomous uncertain and stochastic systems with multiple delays, which describe a financial system involving the interest rate, the investment demand and the price index. For the deterministic model associated to the uncertain financial system, we set the conditions for the existence of the delay parameter value for which the model displays a Hopf bifurcation. For the stochastic system, we identify the differential equations for the mean value as well as for the square mean value. The last part of the paper includes numerical simulations and conclusions.
This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stochastic model, the dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given to illustrate our theoretical results.
The paper is a conceptual approach to education for sustainable development using an e-learning platform. It starts from the observed reality that all education stakeholders need a learning environment where they can have access to knowledge, collaborate and share their experience, as a survey conducted among students and companies in Timisoara, Romania, region shows. The proposed multi-stakeholder environment accommodates two sections: the learning environment mostly dedicated to students, trainees, tutors and mentors and the virtual sustainability centre that is dedicated to on-line meetings, workshops, counselling, etc. Durable learning is supported by a range of written digital and multimedia resources, including pre-recorded on-line tutoring, videos and games. To engage online learners, various gamification techniques were used in the course design phase, such as recording and presenting the learner’s progress, role-playing and similar. The article presents a conceptual design of the learner’s journey and a mapping from gamification concepts to Moodle LMS elements.
Keywords: E-learning, education, sustainable development, gamification, LMS
This paper studies the dynamic behavior of asset prices using a chartist-fundamentalist model with two speculative markets. To this effect, we employ a differential system with delays à la Dibeh (2007) to describe the price dynamics and we assume that the two markets are coupled via diffusive coupling terms. We study two different time delay cases, namely, when both markets experience the same time delay and when the time delay is different across markets. First, we theoretically determine that the equilibrium exists and investigate its stability. Second, we establish the general conditions for the existence of local Hopf bifurcations and analyze their direction and stability. The common conclusion from both the delay scenarios we consider is that coupled speculative markets with heterogeneous agents in each, but with different price dynamics, can be synchronized through diffusive coupling. Finally, we provide some numerical illustrations to confirm our theoretical findings.
The paper analyses a model that describes a wireless access network with one bottleneck router and n ≥ 2 TCP flows described by a nonlinear dynamical system. The equilibrium point is determined for the general case. For the particular case n = 2 the periodic solutions are examined, when the round trip time is considered as bifurcation parameter. The conditions for the local asymptotic stability of the equilibrium point are given. In the last part, using Maple and Matlab, the numerical example verifies the theoretical results and some conclusions and future directions are shown.
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