Propagation of shock wave of the time fractional Gardner Burger equation in a multicomponent plasma using novel analytical method

The time-fractional Gardner Burger (TFGB) equation is an efficient model for studying nonlinear fluctuations of different types of wave profiles, such as the gravity solitary waves in the ocean, ion-acoustic wave (IAW) in a plasma environment, etc. Here, to build an example of the existence of the classical Gardner Burger (GB) equation, a multi-component plasma environment is considered and a classical GB equation is derived by employing reductive perturbation technique (RPT) from the basic governing equation. Further, the classical GB equation is converted into the TFGB equation by applying Agrawal’s approach, where the Riesz fractional derivative is adopted on the time-fractional term. A new approach using the improved Bernoulli sub-equation function method (IBSEFM) is carried out to solve the TFGB equation. Finally, some $2D$ and $3D$ graphs are plotted through which the physical structures of the solution are explored and the effect of the Burgers term and fractional order of the equation are determined.

The Impact of Geopolitical Risk on Systemic Risk Spillover in Commodity Market: An EMD-Based Network Topology Approach

Since the financialization of commodities, portfolio investments have become an important tool for investors to diversify risks. However, due to the nonlinear fluctuations brought about by extreme events, investors face more difficulties in the choice of risk portfolio. We adopt empirical mode decomposition and STVAR model, along with the basis data of optimized original sample interval. In addition, we retain the mature research of multiscale systemic risk under frequency and divide the dimension of systemic risk into two states. When frequency is combined with states, the risk spillover center undergoes subversive changes, particularly in the longest term, and metals become the risk spillover center, substituting the energy commodity, on the condition that the compositions of extreme value add persuasive power to the perspective of long term. We proposed that the joint fluctuation of agricultural commodities and energy commodities makes the former become another important risk spillover point. For investors, holding period and portfolio both need to be considered.

IRREGULAR DYNAMICS IN THE AGENT-BASED MIGRATION MODEL

The article is devoted to modeling the dynamics of migration at the regional level. In the context of the transition to a post-industrial society, population migration becomes more dynamic, which requires improving approaches to its forecasting and makes significant the study of personal strategies for choosing the time of migration and the host region by agents. Different strategies of agents lead to the emergence of migrant strata with dynamically changing number, unevenly distributed among the receiving regions. As a result, it can observed nonlinear fluctuations in the number of migrants, for the study of which simulation modeling tools are relevant. This research is devoted to the study of the migration processes complex dynamics by the method of agent-based modeling. The simulation is based on the assumption that a migrant, when choosing a region, follows a strategy, characteristic of his age group, which in the long end directly affects the distribution of the number of migrants of various cohorts and the total number of migrants in the region. At this, the strategy choice is determined by socio-economic characteristics of the regions: different levels of economic, social and environmental attractiveness. The authors hypothesized that different strategies of migration behavior can lead to complex migration dynamics. To test the hypothesis, the authors built a basic agent-based model of migration for three regions, which takes into account various strategies of agents' migration behavior, including the choice of a region with the highest economic, social or environmental level of attractiveness. The result of numerical experiments shows that a combination of various strategies for choosing a region with a change in the age structure of migrants leads to periodic and complex regimes of migration dynamics. The authors have found the conditions under which complex dynamics in the model occurs in the short - and medium-term periods.

On the Question of Nonlinear Fluctuations of Heavy Ropes

Due to the methods of the dynamics of curvilinear motion the system of nonlinear differential equations describing two-dimensional arbitrary displacements of a heavy rope, one end of which is free, and the other is fastened is obtained. The problem is solved in the language of displacement vector ()()(),,,xyxtxtxtξξξ=+ij, where (),xxtξ and (),yxtξ accordingly, arbitrary offsets of the rope points in the axes of coordinates. It is shown that in the limit of small oscillations the obtained equations are reduced to the description of the weak offsets of the horizontal string fixed on both ends, and small displacements of the heavy vertical filament, fluctuating due to the force of gravity. The main goal of the paper is the mathematical description of the strong non-equilibrium dynamic systems.