Endogenous Cycles in a Keen--Goodwin Model with Minsky Debt
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910088169521152 |
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| author | Albarrán-García, Roberto Alvarez-Ramírez, Martha García-Azpeitia, Carlos |
| author_facet | Albarrán-García, Roberto Alvarez-Ramírez, Martha García-Azpeitia, Carlos |
| contents | We analyze a three-dimensional Keen--Goodwin model that couples wage--employment dynamics with Minsky-style private debt. At zero real interest the interior equilibrium is nonhyperbolic and organized by a two-dimensional center manifold foliated by neutral Goodwin cycles. Introducing a small positive interest rate unfolds this degeneracy: we derive an explicit Hopf condition, prove persistence of the center manifold as a normally hyperbolic attracting surface, and obtain first-order amplitude and frequency corrections for the emergent limit cycle via phase--amplitude reduction. Numerical simulations support the asymptotic predictions and demonstrate how interest rates determine and modulate endogenous business cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Endogenous Cycles in a Keen--Goodwin Model with Minsky Debt Albarrán-García, Roberto Alvarez-Ramírez, Martha García-Azpeitia, Carlos Dynamical Systems Classical Analysis and ODEs 37G15, 37C75, 91B62, 34C23 We analyze a three-dimensional Keen--Goodwin model that couples wage--employment dynamics with Minsky-style private debt. At zero real interest the interior equilibrium is nonhyperbolic and organized by a two-dimensional center manifold foliated by neutral Goodwin cycles. Introducing a small positive interest rate unfolds this degeneracy: we derive an explicit Hopf condition, prove persistence of the center manifold as a normally hyperbolic attracting surface, and obtain first-order amplitude and frequency corrections for the emergent limit cycle via phase--amplitude reduction. Numerical simulations support the asymptotic predictions and demonstrate how interest rates determine and modulate endogenous business cycles. |
| title | Endogenous Cycles in a Keen--Goodwin Model with Minsky Debt |
| topic | Dynamical Systems Classical Analysis and ODEs 37G15, 37C75, 91B62, 34C23 |
| url | https://arxiv.org/abs/2603.29178 |