Crisis cycles in the slightly unstable block random model

ABSTRACT

The paper proposes a new approach for studying the time to time appearing breakdowns in economy. Block random model can describe stability of large complicated systems with variable number of participants. Theoretical background of the model is given by a theorem about the eigenvalues of block random matrices [Juhász F. On the characteristic values of non-symmetric block random matrices. J Theoret Probab. 1990;67:199–205; On the structural eigenvalues of block random matrices. Linear Algebra Appl. 1996;246:225–231]. The model takes into account not only effects of participants but of groups formed from them as well. Slight instability means group level stability and participant level instability [Juhász F. On the turbulence of slightly unstable block random systems. In: Taylor C, et al., editors. Numerical methods for laminar and turbulent flow. Atlanta; 1995. p. 113–121]. Lability index of block random systems is introduced for measuring instability. It is showed that lability index of a slightly unstable block random model is growing while number of participants increases. Alteration in the number of participants makes it possible to describe crisis cycles.

KEYWORDS:

• Random matrices
• eigenvalues
• dynamical systems
• Lyapunov stability
• turbulence
• economics

SUBJECT CLASSIFICATION CODES:

• 15B52
• 15A18
• 76F20
• 93D05
• 93E15

Acknowledgements

I wish to thank Zsuzsa Juhász for the calculations and Károly Mályusz for his useful advices.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. One can imagine that the first group consists of the banks (Group1), the second group consists of multinational companies (Group2), and the third is formed by small- and medium-sized companies (Group3). In the case of banks the amount of loans can play the role of capital.