Dynamics of interacting populations

Weidlich, W. Haag, G. (1983). Concepts and models of a quantitative sociology The dynamics of interacting populations), (Springer Series in Synergetics, Vol. 14). Springer Verlag, Berlin. 

The "dynamics of interacting populations" to be investigated in this book then consist of a theory concerning the structural development of this socioconfiguration, or of quantities derived from it, with time. 

In 1914, F. W. Lanchester introduced a set of coupled ordinary differential equations-now commonly called the Lanchester Equationsl (LEs)-as models of attrition in modern warfare. Similar ideas were proposed around that time by [chaseSS] and [osip95]. These equations are formally equivalent to the Lotka-Volterra equations used for modeling the dynamics of interacting predator-prey populations [hof98]. The LEs have since served as the fundamental mathematical models upon which most modern theories of combat attrition are based, and are to this day embedded in many state-of-the-art military models of combat. [Taylor] provides a thorough mathematical discussion. 

This paper reviws the classification and dynamics of interaction between pairs of microbial populations inhabiting a common environment. A few cases of interaction between three or more populations are considered, also. The nature of the scheme of classification of interaction is described and its utility as well as its weaknesses are mentioned. 

Dynamic behavior and oscillations are also found in nature, such as predator-prey interactions. A classical example of interacting populations is shown in Figure 4.10.30 for the snowshoe hare and the Canadian lynx, a specialist predator. The lynx-hare... 

W. Weidlich, G. Haag Dynamics of Interacting Groups with Application to the Migration of Population , in Lectures and Tutorials, Vol. 11 (Oldenburg, Munich 1980)... 

He describes molecular populations mathematically in the way physicists calculate classical dynamic systems. Very exact dynamic equations are devised, while the laws of interaction are left very general. This leads to a general theory of molecular systems, which makes it possible to define what is understood by the origin of metabolism (Dyson, 1999). 

The simulation of the population structure and dynamics of autotrophs and phagotrophs is another important interaction that can be modeled to test for effects of pollutant stress. A standard approach is the use of a flnite-population-difference model. The model assumes that the population change of a species in a specific period is equal to the species population multiplied by an intrinsic coefficient of rate of change. The rate coefficients are difficult to define without extensive data. The task is further complicated because a consistent feature of... 

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

The decay of the B state population due to predissociation is linked to the dynamics of the vibrational relaxation. It could be shown that a longer relaxation time also resulted in a delayed predissociation of the B state iodine molecules. As soon as the vibrational relaxation is completed, the predissociation is solely determined by the coupling strength between the bound B and the repulsive a/a1 states. The coupling of these states is again a function of the interaction with the surrounding cage. 

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