• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.393-407
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• 2022

In this paper, a diffusive predator-prey system with Beddington DeAngelis functional response and the modified Leslie-Gower type predator dynamics when a prey population is infected is considered. The predator is assumed to predate both the susceptible prey and infected prey following the Beddington-DeAngelis functional response and Holling type II functional response, respectively. The predator follows the modified Leslie-Gower predator dynamics. Both the prey, susceptible and infected, and predator are assumed to be distributed in-homogeneous in space. A reaction-diffusion equation with Neumann boundary conditions is considered to capture the dynamics of the prey and predator population. The global attractor and persistence properties of the system are studied. The priori estimates of the non-constant positive steady state of the system are obtained. The existence of non-constant positive steady state of the system is investigated by the use of Leray-Schauder Theorem. The existence of non-constant positive steady state of the system, with large diffusivity, guarantees for the occurrence of interesting Turing patterns.

• KDI Journal of Economic Policy
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• v.32 no.3
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• pp.1-32
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• 2010

The global financial crisis has exerted enormous impacts on the attainment of inflation target in Korea. The annual average CPI inflation was 3.3% during the targeting period of 2007-2009 and the target was $3.0{\pm}0.5%$. Thus Korea has succeeded in keeping annual average CPI inflation just below the upper limit of the 2007-2009 target under the global crisis. This paper intends to evaluate the performance of the inflation targeting system in Korea. First, it estimates the conventional call rate reaction equation under the global crisis and finds that the policy interest rates never reacted to expected inflation, output gap, and won/dollar exchange rate, as expected by theory. Second, it identifies the shock of global financial crisis into core and non-core, applying the structural VAR model. The core shock was defined to have no (medium- to) long-run impact on real output. The core shock was identified to have the character of the demand shock, since it has the positive impact on the inflation and output in the short run. The structural core inflation due to core shock was an attractor of headline inflation, not vice versa. Therefore, the structural core inflation that reflects the demand-side shock would be the better intermediate target for the final headline inflation target than the official core inflation that excludes the volatile inflation of agricultural and oil-related products. During the inflation targeting period of 2007-2009, the structural core inflation was more volatile than the official core inflation, because the global crisis has very large negative impacts on the domestic demand as well as the prices of agricultural and oil-related products. This paper shows that the negative core shock during the fourth quarter of 2008 was larger than that in the financial crisis in 1998. But the core shock turned into positive very quickly in 2009, as the Korean economy recovered very quickly from crisis. The volatile changes in structural core inflation suggests that the Bank of Korea barely managed to attain the 2007-2009 inflation target, owing to the very large negative impacts of the global financial crisis on the domestic demand. It also suggests that the rapid rise in core inflation with the rapid recovery of the Korean economy will lead to rapid rise in headline inflation.