Noise-Induced Phenomena in the Kaldor Business Cycle Model

Abstract

The periodic behavior of macroeconomic indicators or business cycles is a common observation in the economic system. In the past, business cycle modeling often involved the use of non-linear economic dynamic theory, general equilibrium theory, and methods to analyze complex systems, such as agent-based modeling and complex network theory. Several studies have shown that crisis and synchronization in business cycles can be modeled using threshold characteristics in the economic systems. In a non-linear system, it is well known that additive noise leads to qualitative transformations in system behavior, such as coherence resonance, stochastic resonance, and noise-induced transitions (referred to as noise-induced phenomena in this study). Recent studies have shown that noise-induced transitions arise in the non-linear economic business cycle model with multiple attractors around the sub-critical Hopf bifurcation. However, the relationship between the threshold characteristics in the economic dynamics and noise-induced phenomena has not been studied. In this study, we focus on the threshold characteristic of the Kaldor business cycle model under the bias of income, and show that coherence resonance and stochastic resonance can be produced as an effect of this threshold characteristic.

Resonance phenomena controlled by external feedback signals and additive noise in neural systems

“…Over decades, many types of synchronization phenomena in nonlinear systems have been explored (reviewed in 1–3 ). Among them, stochastic resonance, in which additive noise enhances the response to weak input signals, has been widely observed in nonlinear systems, such as global climate 4 , economic 5 , electric 6 , and biological 7–10 systems. In particular, regarding recent studies about stochastic resonance in neural systems, we reported that spike-timing-dependent plasticity might be enhanced by stochastic resonance, and the enhancement depends on neural spiking patterns 11 .…”

Recent Trends of Controlling Chaotic Resonance and Future Perspectives

“…In a wide range of non-linear systems, it is known that additive stochastic noise and internal dynamical fluctuation enhance the ordering of spatio-temporal behaviors, such as the emergence of periodicity and synchronization (as reviewed in [1][2][3][4][5][6]). Among these phenomena, stochastic resonance is a phenomenon in which the effects of additive noise strengthen the signal response against weak input signals in the non-linear systems with a specific barrier or threshold [7][8][9] (as reviewed in [1,2,4,10,11]). Recent studies on stochastic resonance have been conducted considering various engineering applications, such as biomedical engineering [12,13], telecommunications [14], and memory storing mechanisms [15][16][17].…”

Chaos-Chaos Intermittency Synchronization Controlled by External Feedback Signals in Chua's Circuits

“…These nonlinear synchronization phenomena are classified according to the sources of fluctuation, i.e., additive stochastic noise and internal deterministic chaos. The former one is called stochastic resonance, which is observed in various kinds of systems, such as climate systems, nonlinear electric circuits, biological systems, and social systems [10]- [17]. The latter one is called chaotic resonance [18], [19], which is observed in systems with chaoschaos intermittency (CCI) where the chaotic orbit appears between separate regions, such as one-dimensional cubic map, Chua's circuit, Lorenz systems, and duffing systems [20], [21] (reviewed in [19], [22]- [24]).…”