The purpose of this paper is to build and analyse a model of unemployment, where jobs search is open to both natives and migrant workers. Markets and government intervention respond jointly to unemployment when creating new jobs. Full employment of resources is the focal point of policy action, stimulating vacancy creation. We acknowledge that policy is implemented with delays, and capture labour market outcomes by building a non-linear dynamic system. We observe jobs separation and matching, and extend our model to an open economy with migration and delayed policy intervention meant to reduce unemployment. We analyse the stability behaviour of the resulting equilibrium for our dynamic system, including models with Dirac and weak kernels. We simulate our model with alternative scenarios, where policy action towards jobs creation considers both migration and unemployment, or just unemployment.

This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stochastic model, the dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given to illustrate our theoretical results.

Green banking has become dominant in academics’ and practitioners’ discourse. The purpose of the research is to investigate whether banks’ attitudes, in deciding to go green, change under the influence of other banks through their mutual interaction and whether hysteresis plays a part in the process. A mathematical model, described by a differential system with time delay, considering three variables, i.e.: green, outsider and undecided banks, is used as a research method. We investigate the local stability of the two equilibrium points. Moreover, we look for the optimal control strategy targeting the undecided banks so that the outsiders’ group diminishes. The main contribution is that the paper sheds more light on the qualitative rather than on the quantitative side of the banking business given that banks’ behaviours are examined when it comes to implementing green policies. The research has policy implications since bank managers can decide whether to follow the greening trends of other banks and bank regulators can use the instrument for tracking the overall changes in banks’ behaviours in this respect.

This article generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is undertaken for the system with general distributed delays. A thorough bifurcation analysis for the distributed delay model with several types of delay kernels is provided. Numerical simulations are carried out for the distributed delays models and for the fractional-order model with discrete delays, which substantiate the theoretical findings. It is shown that these models are able to capture the vital mechanisms of the HPA system.