# American Institute of Mathematical Sciences

July  2020, 7(3): 175-184. doi: 10.3934/jdg.2020012

## Emerging patterns in inflation expectations with multiple agents

 1 Research Group in Economic Dynamics, Universidad de la República, Montevideo, Uruguay 2 IIESS (UNS - Conicet) and Departamento de Economía, Universidad Nacional del Sur, San Andrés 800, Bahía Blanca 8000, Argentina

* Corresponding author: ealvarez@ccee.edu.uy

Received  February 2020 Revised  April 2020 Published  July 2020

Macroeconomic theory and central Banks' policy recommendations have analyzed for decades the link between the expected value of future inflation and its subsequent realization. Agents' inflation expectations have thus become a fundamental input of the economic policy: they allow to know if economic agents are synchronized with the policies and allow the Central Banks to anticipate the market trends. In this paper, we found evidence for the case of Uruguay of a discrepancy between the distribution of agents' inflation expectations and the distribution expected by traditional models. A first consequence is an increase in uncertainty in the estimates; problems related to its asymptotic distribution and the assumptions that arise from this aggregate distribution are analyzed. Another consequence is related to the existence of a structure in the data and the notion of equilibrium in the model. It is concluded that a discussion regarding the nature of the economic phenomenon is essential for the correct specification of the model studied.

Citation: Emiliano Alvarez, Silvia London. Emerging patterns in inflation expectations with multiple agents. Journal of Dynamics & Games, 2020, 7 (3) : 175-184. doi: 10.3934/jdg.2020012
##### References:
 [1] T. Assenza, P. Heemeijer, C. H. Hommes and D. Massaro, Individual expectations and aggregate macro behavior, Tinbergen Institute Discussion Paper 13-016/II, (2013), 59 pp. doi: 10.2139/ssrn.2200424.  Google Scholar [2] J. M. Berk, The Preparation of Monetary Policy: Essays on a Multi-Model Approach, Financial and Monetary Policy Studies, 35, Kluwer Academic Publishers, Boston, 2001. Google Scholar [3] G. E. P. Box, Science and statistics, J. Amer. Statist. Assoc., 71 (1976), 791-799.  doi: 10.1080/01621459.1976.10480949.  Google Scholar [4] W. A. Branch, Sticky information and model uncertainty in survey data on inflation expectations, Journal of Economic Dynamics and Control, 31 (2007), 245-276.  doi: 10.1016/j.jedc.2005.11.002.  Google Scholar [5] W. A. Brock and S. N. Durlauf, Discrete choice with social interactions, Rev. Econom. Stud., 68 (2001), 235-260.  doi: 10.1111/1467-937X.00168.  Google Scholar [6] W. A. Brock and C. H. Hommes, A rational route to randomness, Econometrica, 65 (1997), 1059-1095.  doi: 10.2307/2171879.  Google Scholar [7] W. A. Brock and C. H. Hommes, Heterogeneous beliefs and routes to chaos in a simple asset pricing model, J. Econom. Dynam. Control, 22 (1998), 1235-1274.  doi: 10.1016/S0165-1889(98)00011-6.  Google Scholar [8] P. Cagan, The monetary dynamics of hyperinflation, in Studies in the Quantity Theory of Money, University of Chicago Press, Chicago and London, 1956, 25–117. Google Scholar [9] J. L. Cardoso and N. Palma, The science of things generally?, in Lionel Robbins's Essay on the Nature and Significance of Economic Science–75th Anniversary Conference Proceedings, Londres, London School of Economics, STICERD, 2009,387–402. Google Scholar [10] J. A. Carlson, Are price expectations normally distributed?, Journal of the American Statistical Association, 70 (1975), 749-754.  doi: 10.1080/01621459.1975.10480299.  Google Scholar [11] Y. G. Chen, Inflation, inflation expectations, and the phillips curve, Technical Report, CBO Working Paper 2019-07, (2019), 58 pp. Google Scholar [12] A. Clauset, C. R. Shalizi and M. E. Newman, Power-law distributions in empirical data, SIAM Review, 51 (2009), 661-703.  doi: 10.1137/070710111.  Google Scholar [13] O. Coibion and Y. Gorodnichenko, Is the phillips curve alive and well after all? Inflation expectations and the missing disinflation, American Economic Journal: Macroeconomics, 7 (2015), 197-232.  doi: 10.3386/w19598.  Google Scholar [14] O. Coibion, Y. Gorodnichenko and R. Kamdar, The formation of expectations, inflation and the phillips curve, Journal of Economic Literature, 56 (2018), 1447-1491.  doi: 10.3386/w23304.  Google Scholar [15] A. Cornea-Madeira, C. Hommes and D. Massaro, Behavioral heterogeneity in US inflation dynamics, Journal of Business & Economic Statistics, 37 (2019), 288-300.   Google Scholar [16] R. Curtin, Inflation expectations and empirical tests: Theoretical models and empirical tests, in Inflation Expectations, Routledge, 2009, 52–79. Google Scholar [17] L. Dräger and M. J. Lamla, Updating inflation expectations: Evidence from micro-data, Economics Letters, 117 (2012), 807-810.   Google Scholar [18] G. W. Evans, C. H. Hommes, B. McGough and I. Salle, Are long-horizon expectations (de-) stabilizing? Theory and experiments, Bank of Canada Staff Working Paper, (2019). Google Scholar [19] E. F. Fama, The behavior of stock-market prices, The Journal of Business, 38 (1965), (1965), 34–105. doi: 10.1086/294743.  Google Scholar [20] A. M. Fasolo and M. S. Portugal, Imperfect rationality and inflationary inertia: A new estimation of the Phillips Curve for Brazil, Estudos Econômicos (São Paulo), 34 (2004), 725–776. Google Scholar [21] E. Fehr and K. M. Schmidt, The economics of fairness, reciprocity and altruism–experimental evidence and new theories, Economics, 20 (2005), 51. doi: 10.1016/S1574-0714(06)01008-6.  Google Scholar [22] S. Frache and R. Lluberas, New information and inflation expectations among firms, BIS Working Papers, 781, (2019), 42 pp. Google Scholar [23] J. E. Gagnon, Long memory in inflation expectations: Evidence from international financial markets, Board of Governors of the Federal Reserve System, 538 (1996). Google Scholar [24] C. S. Gillespie, Fitting heavy tailed distributions: The poweRlaw package, Journal of Statistical Software, 64 (2015), 1-16.   Google Scholar [25] A. P. Kirman, Individual and aggregate behaviour: Of ants and men, Complexity and the Economy: Implications for Economic Policy, (2005), 33–53. doi: 10.1016/j.jmateco.2004.08.001.  Google Scholar [26] A. Leijonhufvud, La naturaleza de una economía, Investigación Económica, 70 (2011), 15-36.  doi: 10.22201/fe.01851667p.2011.277.37315.  Google Scholar [27] P. Lévy, Calcul des Probabilités, PCMI collection, Gauthier-Villars, 1925. Google Scholar [28] S. London and F. Tohmé, Economic evolution and uncertainty: Transitions and structural changes, Journal of Dynamics & Games, 6 (2019), 149-158.   Google Scholar [29] B. Mandelbrot, The variation of certain speculative prices, The Journal of Business, 36 (1963), 394-419.   Google Scholar [30] N. G. Mankiw and R. Reis, Sticky information versus sticky prices: A proposal to replace the new keynesian phillips curve, The Quarterly Journal of Economics, 117 (2002), 1295-1328.  doi: 10.3386/w8290.  Google Scholar [31] R. D. McKelvey and T. R. Palfrey, Quantal response equilibria for normal form games, Games and Economic Behavior, 10 (1995), 6-38.  doi: 10.1006/game.1995.1023.  Google Scholar [32] J. F. Muth, Rational expectations and the theory of price movements, Econometrica: Journal of the Econometric Society, (1961), 315–335. doi: 10.2307/1909635.  Google Scholar [33] M. E. Newman, Power laws, pareto distributions and zipf's law, Contemporary Physics, 46 (2005), 323-351.  doi: 10.1080/00107510500052444.  Google Scholar [34] J. P. Nolan, Fitting data and assessing goodness-of-fit with stable distributions, Applications of Heavy Tailed Distributions in Economics, Engineering and Statistics, Washington DC, 1999. Google Scholar [35] D. Phan, M. B. Gordon, and J.-P. Nadal, Social interactions in economic theory: An insight from statistical mechanics, in Cognitive Economics, Springer, 2004,335–358. Google Scholar [36] S. Rinke, M. Busch and C. Leschinski, Long memory, breaks, and trends: On the sources of persistence in inflation rates, Hannover Economic Papers (HEP), (2017). Google Scholar [37] J. Royuela-del Val, et al., Libstable: Fast, parallel, and high-precision computation of $\alpha$-stable distributions in r, c/c++, and matlab, Journal of Statistical Software, 78 (2017). Google Scholar [38] S. S. Shapiro and M. B. Wilk, An analysis of variance test for normality (complete samples), Biometrika, 52 (1965), 591-611.  doi: 10.1093/biomet/52.3-4.591.  Google Scholar [39] C. A. Sims, Implications of rational inattention, Journal of monetary Economics, 50 (2003), 665-690.  doi: 10.1016/S0304-3932(03)00029-1.  Google Scholar [40] J. Smith and M. McAleer, Alternative procedures for converting qualitative response data to quantitative expectations: An application to australian manufacturing, Journal of Applied Econometrics, 10 (1995), 165-185.  doi: 10.1002/jae.3950100206.  Google Scholar [41] L. E. Svensson, Inflation forecast targeting: Implementing and monitoring inflation targets, European Economic Review, 41 (1997), 1111-1146.  doi: 10.3386/w5797.  Google Scholar [42] J. B. Taylor, Discretion versus policy rules in practice, in Carnegie-Rochester Conference Series on Public Policy, 39, Elsevier, 1993,195–214. doi: 10.1016/0167-2231(93)90009-L.  Google Scholar [43] H. Theil, Economic Forecasts and Policy, North-Holland, 1958. Google Scholar [44] F. Tohmé, C. Dabús and S. London, Processes of evolutionary self-organization in high inflation experiences, in New Tools of Economic Dynamics, Springer, 2005,357–371. Google Scholar [45] M. Woodford, Imperfect common knowledge and the effects of monetary policy, Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps, (2003), 25. doi: 10.3386/w8673.  Google Scholar

show all references

##### References:
 [1] T. Assenza, P. Heemeijer, C. H. Hommes and D. Massaro, Individual expectations and aggregate macro behavior, Tinbergen Institute Discussion Paper 13-016/II, (2013), 59 pp. doi: 10.2139/ssrn.2200424.  Google Scholar [2] J. M. Berk, The Preparation of Monetary Policy: Essays on a Multi-Model Approach, Financial and Monetary Policy Studies, 35, Kluwer Academic Publishers, Boston, 2001. Google Scholar [3] G. E. P. Box, Science and statistics, J. Amer. Statist. Assoc., 71 (1976), 791-799.  doi: 10.1080/01621459.1976.10480949.  Google Scholar [4] W. A. Branch, Sticky information and model uncertainty in survey data on inflation expectations, Journal of Economic Dynamics and Control, 31 (2007), 245-276.  doi: 10.1016/j.jedc.2005.11.002.  Google Scholar [5] W. A. Brock and S. N. Durlauf, Discrete choice with social interactions, Rev. Econom. Stud., 68 (2001), 235-260.  doi: 10.1111/1467-937X.00168.  Google Scholar [6] W. A. Brock and C. H. Hommes, A rational route to randomness, Econometrica, 65 (1997), 1059-1095.  doi: 10.2307/2171879.  Google Scholar [7] W. A. Brock and C. H. Hommes, Heterogeneous beliefs and routes to chaos in a simple asset pricing model, J. Econom. Dynam. Control, 22 (1998), 1235-1274.  doi: 10.1016/S0165-1889(98)00011-6.  Google Scholar [8] P. Cagan, The monetary dynamics of hyperinflation, in Studies in the Quantity Theory of Money, University of Chicago Press, Chicago and London, 1956, 25–117. Google Scholar [9] J. L. Cardoso and N. Palma, The science of things generally?, in Lionel Robbins's Essay on the Nature and Significance of Economic Science–75th Anniversary Conference Proceedings, Londres, London School of Economics, STICERD, 2009,387–402. Google Scholar [10] J. A. Carlson, Are price expectations normally distributed?, Journal of the American Statistical Association, 70 (1975), 749-754.  doi: 10.1080/01621459.1975.10480299.  Google Scholar [11] Y. G. Chen, Inflation, inflation expectations, and the phillips curve, Technical Report, CBO Working Paper 2019-07, (2019), 58 pp. Google Scholar [12] A. Clauset, C. R. Shalizi and M. E. Newman, Power-law distributions in empirical data, SIAM Review, 51 (2009), 661-703.  doi: 10.1137/070710111.  Google Scholar [13] O. Coibion and Y. Gorodnichenko, Is the phillips curve alive and well after all? Inflation expectations and the missing disinflation, American Economic Journal: Macroeconomics, 7 (2015), 197-232.  doi: 10.3386/w19598.  Google Scholar [14] O. Coibion, Y. Gorodnichenko and R. Kamdar, The formation of expectations, inflation and the phillips curve, Journal of Economic Literature, 56 (2018), 1447-1491.  doi: 10.3386/w23304.  Google Scholar [15] A. Cornea-Madeira, C. Hommes and D. Massaro, Behavioral heterogeneity in US inflation dynamics, Journal of Business & Economic Statistics, 37 (2019), 288-300.   Google Scholar [16] R. Curtin, Inflation expectations and empirical tests: Theoretical models and empirical tests, in Inflation Expectations, Routledge, 2009, 52–79. Google Scholar [17] L. Dräger and M. J. Lamla, Updating inflation expectations: Evidence from micro-data, Economics Letters, 117 (2012), 807-810.   Google Scholar [18] G. W. Evans, C. H. Hommes, B. McGough and I. Salle, Are long-horizon expectations (de-) stabilizing? Theory and experiments, Bank of Canada Staff Working Paper, (2019). Google Scholar [19] E. F. Fama, The behavior of stock-market prices, The Journal of Business, 38 (1965), (1965), 34–105. doi: 10.1086/294743.  Google Scholar [20] A. M. Fasolo and M. S. Portugal, Imperfect rationality and inflationary inertia: A new estimation of the Phillips Curve for Brazil, Estudos Econômicos (São Paulo), 34 (2004), 725–776. Google Scholar [21] E. Fehr and K. M. Schmidt, The economics of fairness, reciprocity and altruism–experimental evidence and new theories, Economics, 20 (2005), 51. doi: 10.1016/S1574-0714(06)01008-6.  Google Scholar [22] S. Frache and R. Lluberas, New information and inflation expectations among firms, BIS Working Papers, 781, (2019), 42 pp. Google Scholar [23] J. E. Gagnon, Long memory in inflation expectations: Evidence from international financial markets, Board of Governors of the Federal Reserve System, 538 (1996). Google Scholar [24] C. S. Gillespie, Fitting heavy tailed distributions: The poweRlaw package, Journal of Statistical Software, 64 (2015), 1-16.   Google Scholar [25] A. P. Kirman, Individual and aggregate behaviour: Of ants and men, Complexity and the Economy: Implications for Economic Policy, (2005), 33–53. doi: 10.1016/j.jmateco.2004.08.001.  Google Scholar [26] A. Leijonhufvud, La naturaleza de una economía, Investigación Económica, 70 (2011), 15-36.  doi: 10.22201/fe.01851667p.2011.277.37315.  Google Scholar [27] P. Lévy, Calcul des Probabilités, PCMI collection, Gauthier-Villars, 1925. Google Scholar [28] S. London and F. Tohmé, Economic evolution and uncertainty: Transitions and structural changes, Journal of Dynamics & Games, 6 (2019), 149-158.   Google Scholar [29] B. Mandelbrot, The variation of certain speculative prices, The Journal of Business, 36 (1963), 394-419.   Google Scholar [30] N. G. Mankiw and R. Reis, Sticky information versus sticky prices: A proposal to replace the new keynesian phillips curve, The Quarterly Journal of Economics, 117 (2002), 1295-1328.  doi: 10.3386/w8290.  Google Scholar [31] R. D. McKelvey and T. R. Palfrey, Quantal response equilibria for normal form games, Games and Economic Behavior, 10 (1995), 6-38.  doi: 10.1006/game.1995.1023.  Google Scholar [32] J. F. Muth, Rational expectations and the theory of price movements, Econometrica: Journal of the Econometric Society, (1961), 315–335. doi: 10.2307/1909635.  Google Scholar [33] M. E. Newman, Power laws, pareto distributions and zipf's law, Contemporary Physics, 46 (2005), 323-351.  doi: 10.1080/00107510500052444.  Google Scholar [34] J. P. Nolan, Fitting data and assessing goodness-of-fit with stable distributions, Applications of Heavy Tailed Distributions in Economics, Engineering and Statistics, Washington DC, 1999. Google Scholar [35] D. Phan, M. B. Gordon, and J.-P. Nadal, Social interactions in economic theory: An insight from statistical mechanics, in Cognitive Economics, Springer, 2004,335–358. Google Scholar [36] S. Rinke, M. Busch and C. Leschinski, Long memory, breaks, and trends: On the sources of persistence in inflation rates, Hannover Economic Papers (HEP), (2017). Google Scholar [37] J. Royuela-del Val, et al., Libstable: Fast, parallel, and high-precision computation of $\alpha$-stable distributions in r, c/c++, and matlab, Journal of Statistical Software, 78 (2017). Google Scholar [38] S. S. Shapiro and M. B. Wilk, An analysis of variance test for normality (complete samples), Biometrika, 52 (1965), 591-611.  doi: 10.1093/biomet/52.3-4.591.  Google Scholar [39] C. A. Sims, Implications of rational inattention, Journal of monetary Economics, 50 (2003), 665-690.  doi: 10.1016/S0304-3932(03)00029-1.  Google Scholar [40] J. Smith and M. McAleer, Alternative procedures for converting qualitative response data to quantitative expectations: An application to australian manufacturing, Journal of Applied Econometrics, 10 (1995), 165-185.  doi: 10.1002/jae.3950100206.  Google Scholar [41] L. E. Svensson, Inflation forecast targeting: Implementing and monitoring inflation targets, European Economic Review, 41 (1997), 1111-1146.  doi: 10.3386/w5797.  Google Scholar [42] J. B. Taylor, Discretion versus policy rules in practice, in Carnegie-Rochester Conference Series on Public Policy, 39, Elsevier, 1993,195–214. doi: 10.1016/0167-2231(93)90009-L.  Google Scholar [43] H. Theil, Economic Forecasts and Policy, North-Holland, 1958. Google Scholar [44] F. Tohmé, C. Dabús and S. London, Processes of evolutionary self-organization in high inflation experiences, in New Tools of Economic Dynamics, Springer, 2005,357–371. Google Scholar [45] M. Woodford, Imperfect common knowledge and the effects of monetary policy, Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps, (2003), 25. doi: 10.3386/w8673.  Google Scholar
Responses to Firms' Expectations Survey, forecasting 12 months ahead. Source: BCU, INE
Estimation of parameters $\alpha, \beta, \gamma$ and $\delta$. In dotted lines 95 % confidence intervals, calculated using bootstrap
Information obtained from Firms' Expectations Survey. Source: BCU-INE, Uruguay. Firms were asked about their inflation expectations in 18 months ahead until July 2013, and about their inflation expectations in 24 months ahead from July 2013. It is related to the change in the monetary policy horizon of the Central Bank of Uruguay
 Variable Firms expectations Data Monthly Span 2012.06 to 2017.12 Surveyed Business financial Managers Observations 522 firms Inflation Forecast Current year 12 months 18 months 24 months
 Variable Firms expectations Data Monthly Span 2012.06 to 2017.12 Surveyed Business financial Managers Observations 522 firms Inflation Forecast Current year 12 months 18 months 24 months
Proportion of months for which the null hypothesis is rejected. P-values obtained by bootstrap in (a) and by the Shapiro-Wilk test in (b)
 12 months 18 to 24 months (a) PL: p-value $<$ 0.05 0 % 1.5 % (b) Normal: p-value $<$ 0.05 100 % 100 %
 12 months 18 to 24 months (a) PL: p-value $<$ 0.05 0 % 1.5 % (b) Normal: p-value $<$ 0.05 100 % 100 %
Sensitivity analysis of the analyzed variables, based on the calculations made by bootstrap
 Variable Expectation 2.5% 25% 50% 75% 97.5 % (a) $\alpha$ 12 months 6.43 7.74 8.46 9.66 17.38 18-24 months 5.55 6.53 7.49 8.46 10.65 (b) $x_{min}$ 12 months 8 10 10 10 14 18-24 months 8 10 10 11 14.35 (c) p-value 12 months 0.3067 0.6908 0.9483 0.9999 1.0000 18-24 months 0.1123 0.6304 0.9497 0.9997 1.0000
 Variable Expectation 2.5% 25% 50% 75% 97.5 % (a) $\alpha$ 12 months 6.43 7.74 8.46 9.66 17.38 18-24 months 5.55 6.53 7.49 8.46 10.65 (b) $x_{min}$ 12 months 8 10 10 10 14 18-24 months 8 10 10 11 14.35 (c) p-value 12 months 0.3067 0.6908 0.9483 0.9999 1.0000 18-24 months 0.1123 0.6304 0.9497 0.9997 1.0000
 [1] Zongyuan Li, Weinan Wang. Norm inflation for the Boussinesq system. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020353 [2] Yuxin Zhang. The spatially heterogeneous diffusive rabies model and its shadow system. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020357 [3] Jiahao Qiu, Jianjie Zhao. Maximal factors of order $d$ of dynamical cubespaces. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 601-620. doi: 10.3934/dcds.2020278 [4] Fanni M. Sélley. A self-consistent dynamical system with multiple absolutely continuous invariant measures. Journal of Computational Dynamics, 2021, 8 (1) : 9-32. doi: 10.3934/jcd.2021002 [5] Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166 [6] Lingju Kong, Roger Nichols. On principal eigenvalues of biharmonic systems. Communications on Pure & Applied Analysis, 2021, 20 (1) : 1-15. doi: 10.3934/cpaa.2020254 [7] Peizhao Yu, Guoshan Zhang, Yi Zhang. Decoupling of cubic polynomial matrix systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 13-26. doi: 10.3934/naco.2020012 [8] Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout, Fatima-Zahrae El Alaoui. Feedback stabilization of bilinear coupled hyperbolic systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020434 [9] Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020451 [10] Xiyou Cheng, Zhitao Zhang. Structure of positive solutions to a class of Schrödinger systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020461 [11] Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030 [12] Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems by stages. Journal of Geometric Mechanics, 2020, 12 (4) : 607-639. doi: 10.3934/jgm.2020029 [13] Lingwei Ma, Zhenqiu Zhang. Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 537-552. doi: 10.3934/dcds.2020268 [14] Peter H. van der Kamp, D. I. McLaren, G. R. W. Quispel. Homogeneous darboux polynomials and generalising integrable ODE systems. Journal of Computational Dynamics, 2021, 8 (1) : 1-8. doi: 10.3934/jcd.2021001 [15] Yuri Fedorov, Božidar Jovanović. Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020375 [16] João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138 [17] Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020444 [18] Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 [19] Meilan Cai, Maoan Han. Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters. Communications on Pure & Applied Analysis, 2021, 20 (1) : 55-75. doi: 10.3934/cpaa.2020257 [20] Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020055

Impact Factor: