Dynamic analysis of a one-prey multi-predator impulsive system with Ivlev-type functional

Considering the Ivlev-type functional response, we develop and analyze a class of one-prey multi-predator system with impulsive effect at different fixed times. Some sufficient conditions ensuring the prey to be extinct are obtained via the Floquent theory and small amplitude perturbation skill. Using the method of comparison involving multiple Laypunov functions, we derive some conditions for the permanence of the system. Numerical simulations of the impulsive system exhibit the rich complex dynamics for the key parameters, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade and crisis.     

Long memory and chaotic models of prices on the London Metal Exchange

Many financial time series exhibit irregular behaviour. Economic theory suggests that this irregular behaviour might be due to the existence of nonlinear dependence in the markets. Thus, economic time series are governed by nonlinear dynamics.The purpose of this paper is to investigate price behaviour in the London Metal Exchange market. Thus, this study will test the two most attractive nonlinear models—long memory and chaos—on six metal commodities to ascertain which model is consistent with the observed metal price nonlinear dynamics.Application of long memory and chaos analysis provides new approaches for assessing the behaviour of metal prices. We identified, in tin, a case of chaos. Our empirical results in the case of aluminium support the long memory hypothesis. A short memory model explains the underlying processes of the nickel and lead returns series, while zinc returns reflect an anti-persistent process. To our knowledge, this is one of the first attempts to apply long memory and chaos analysis in the evaluation of the behaviour of metal prices.     

Developing a chaotic pattern of dynamic risk definition for solving hazardous material routing-locating problem

In the case of determining routes and locations for constructing distribution centers on hazardous materials (Hazmat) transportation, risk and cost are considered as the main attributes for developing mathematical models. Since, Hazmat transport risk may be defined as a chaotic factor, using dynamic risk changes the selected routes and optimized locations for constructing distribution centers.In the present paper, an iterative procedure has been proposed to determine the best routes and optimized locations of distribution centers for transporting hazardous materials based on the concept of chaos theory in which hazmat transport risk is defined as a dynamic variable. A mathematical model has been developed for solving Hazmat routing and locating problems, simultaneously. Daily transport risk, defined as a chaotic variable, is iteratively updated using one-dimensional logistic map equation over the time period (year). An experimental road network, consists of eighty nine nodes and one hundred and three two-way edges, has been selected for analytical process and model validation. Results revealed that although different amounts of risk and cost priorities change optimized locations of distribution centers and their associated supplies, but the most frequent set of optimized centers remains independent. Therefore, the proposed procedure is capable to determine the best routes and optimized locations for distributing hazardous materials. While risk is iteratively updated over a specific time period, results show that the main property of chaos theory known as dependency upon initial condition would not be a serious concern for decision makers who are dealing with Hazmat management.     

Nonlinear time series analysis of ground-level ozone dynamics in Southern Taiwan

The ozone pollution at ground level in rural and urban areas has been a long-standing problem in the world. This paper focuses on estimating self-affined nature of nonlinearity of ground-level peak ozone time series, which is analyzed by two nonlinear fractal statistical methods, including R/S analysis and BDS test. To explore the underlying structure of ozone observations at ground level and improve the forecasting capacity in urban region, practical implementation was assessed by a case study via collecting and analyzing the monitoring data at Chaojhou and Zenwu in the Kaohsiung metropolitan region, Taiwan. Based on R/S analysis, the time series can be identified as persistent and long-memory processes with Hurst exponents of both about 0.75. In addition, the V statistics specifies possible fluctuation cycle lengths of 32, 170, and 420 day simultaneously. Such results are consistent with the regional meteorological conditions leading to help characterize the regional scale ozone behavioral trend. Furthermore, the BDS test results confirm a strong nonlinearity of both time series associated with these two cities. Yet in both cases, nonlinearity implies chaos. The R/S analysis and BDS test provide strong evidence for nonlinearity and fractality of ozone time series due to noisy chaos, and we could not rule out the possibility of deterministic chaos in tropospheric ozone system.