Keywords
chaos, environmental interface, logistic equation, energy balance equation, coupled asymmetric logistic maps
Start Date
1-7-2008 12:00 AM
Abstract
The field of environmental sciences is abundant with various interfaces and it is the right place for application of new fundamental approaches leading towards better understanding of environmental phenomena. For example, following definition of environmental interface by Mihailovic and Balaž [2007], such interface can be placed between natural or artificially built surfaces and atmosphere. In this case, visible radiation provides almost all of the energy received on the environmental interface. Since all the energy transfer processes occurs in the finite time interval the energy balance equation for this environmental interface can be written in terms of finite differences of ground and air temperatures and then, under some conditions, further transformed into the logistic equation [Mihailovic et al., 2001]. In the case of the two interacting environmental interfaces, we have a higher-dimensional complex system. The chaos in a higher dimensional system is one of the focal subject of physics today. One way, in studying this complex system, naturally leads to the model of coupled logistic maps with different strength parameters. In this paper, we report the results of numerical investigation on the system of two logistic maps, representing energy exchange on environmental interfaces, with different strength parameters such that the one map lies in a period one stable attractor or a bifurcation point and the other in chaotic region when decoupled.
Two Interacting Environmental Interfaces: Bifurcation in Coupled Asymmetric Logistic Maps
The field of environmental sciences is abundant with various interfaces and it is the right place for application of new fundamental approaches leading towards better understanding of environmental phenomena. For example, following definition of environmental interface by Mihailovic and Balaž [2007], such interface can be placed between natural or artificially built surfaces and atmosphere. In this case, visible radiation provides almost all of the energy received on the environmental interface. Since all the energy transfer processes occurs in the finite time interval the energy balance equation for this environmental interface can be written in terms of finite differences of ground and air temperatures and then, under some conditions, further transformed into the logistic equation [Mihailovic et al., 2001]. In the case of the two interacting environmental interfaces, we have a higher-dimensional complex system. The chaos in a higher dimensional system is one of the focal subject of physics today. One way, in studying this complex system, naturally leads to the model of coupled logistic maps with different strength parameters. In this paper, we report the results of numerical investigation on the system of two logistic maps, representing energy exchange on environmental interfaces, with different strength parameters such that the one map lies in a period one stable attractor or a bifurcation point and the other in chaotic region when decoupled.
