Rabinovich-Fabrikant system in view point of KCC theory in Finsler geometry

References

• P. L. Antonelli, Handbook of Finsler geometry I, II, Kluwer Academic Publishers, Boston/ Dordrecht, 2003.
   Google Scholar
• P. L. Antonelli, R. S. Ingarden, M. Matsumoto, The theories of sprays and Finsler spaces with application in physics and biology, Kluwer Acad. Publisher, Dordrecht/Boston/London, 1993.
   Google Scholar
• P. L. Antonelli, Equivalence problem for systems of second order ordinary differential equations, Encyclopedia of mathematics, Kluwer Acad. Publishers, Dordrecht, 2000.
   Google Scholar
• C. G. Boehmer, T. Harko and S. V. Sabau, Jacobi stability analysis of Dynamical systems - Applications in Gravitation and Cosmology, Adv. Theor. Math. Phys., 16 (2012) 1145-1196. doi: 10.4310/ATMP.2012.v16.n4.a2
   Web of Science ®Google Scholar
• D. Bao, S. S. Chern, Z. Shen, An Introduction to Riemann-Finsler Geometry , Graduate Texts in Mathematics, vol. 200, Springer, NewYork, 2000. doi: 10.1007/978-1-4612-1268-3
   Google Scholar
• E. Cartan, Observations sur le memoire precedent, Math. Zeitschrift, 37 (1933) 619-622. doi: 10.1007/BF01474603
   Google Scholar
• S. S. Chern, Sur la geometrie dn systeme d’equations differentielles du second ordre, Bull. Sci. Math., 63 (1939) 206-249.
   Google Scholar
• M. F. Danca and G. Chen, Bifurcation and chaos in a complex model of dissipative medium, Int. J. Bifurcation and Chaos, 14 (2004) 3409. doi: 10.1142/S0218127404011430
   Web of Science ®Google Scholar
• M. F. Danca, M. Feckan, N. Kuznetsov and G. Chen, Looking more closely to the Rabinovich-Fabrikant system, Int. J. Bifurcation and Chaos, 26 (2) (2016) 1650038. doi: 10.1142/S0218127416500383
   Web of Science ®Google Scholar
• M. F. Danca, Hidden transient chaotic attractors of Rabinovich-Fabrikant system, Nonlinear Dyn., 86(2) (2016) 1263-1270. doi: 10.1007/s11071-016-2962-3
   Web of Science ®Google Scholar
• M. F. Danca, N. Kuznetsov and G. Chen, Unusual dynamics and hidden attractors of the Rabinovich-Fabrikant system, Nonlinear Dyn., 88 (2017) 791-805. doi: 10.1007/s11071-016-3276-1
   Web of Science ®Google Scholar
• M. K. Gupta, C. K. Yadav, Jacobi stability analysis of Rikitake system, Int. J. Geo. methods mod. Phys., 13 (07) (2016) 1650098. doi: 10.1142/S0219887816500985
   Google Scholar
• M. K. Gupta, C. K. Yadav, Jacobi stability analysis of Rossler system, Int. J. Bifurcation and Chaos, 27 (04) (2017) 1750056. doi: 10.1142/S0218127417500560
   Google Scholar
• M. K. Gupta, C. K. Yadav, Jacobi stability analysis of modified Chua Circuit, Int. J. Geo. methods mod. Phys., 14 (06) (2017) 1750089. doi: 10.1142/S021988781750089X
   Google Scholar
• M. K. Gupta, C. K. Yadav, KCC theory and its application in a tumor growth model. Math Meth Appl Sci. 2017; 1-18. https://doi.org/10.1002/mma.4542.
   Web of Science ®Google Scholar
• T. Harko, C. Y. Ho, C. S. Leung, S. Yip, Jacobi stability analysis of Lorenz system, Int. J. Geo. methods mod. Phys., 12 (07) (2015) 1550081. doi: 10.1142/S0219887815500814
   Google Scholar
• T. Harko, P. Pantaragphong, S. V. Sabau, Kosambi-Cartan-Chern (KCC) theory for higher order dynamical systems, Int. J. Geo. methods mod. Phys., 13 (04) (2016) 1650014. doi: 10.1142/S0219887816500146
   Google Scholar
• D. D. Kosambi, Parallelism and path-space, Math. Zeitschrift, 37 (1933) 608-618.
   Google Scholar
• R. Miron, D. Hrimiuc, H. Shimada, S. V. Sabau, The geometry of Hamilton and Lagrange spaces, Kluwer Acad. Publ., Dordrecht, Boston, 2001.
   Google Scholar
• M. I. Rabinovich and A. L. Fabrikant, Stochastic self modulation of waves in nonequilibriun media, Sov. Phys. JETP, 50 (02) (1979) 311–317.
   Google Scholar
• Q. I. Rahman and G. Schmeisser, Analytic theory of polynomials. London Mathematical Society Monographs. New series 26. Oxford, Oxford University Press, 2002.
   Google Scholar
• A. Ray, P. Saha and A. R. Chowdhury, Competitive mode and topological properties of nonlinear systems with hidden attractor, Nonlinear Dyn, DOI 10.1007/s11071-017-3357-9.
   Web of Science ®Google Scholar
• S. V. Sabau, Some remarks on jacobi stability, Nonlinear Analysis, 63 (2005) e143-e153. doi: 10.1016/j.na.2005.02.061
   Web of Science ®Google Scholar
• S. V. Sabau, Systems biology and deviation curvature tensor, Nonlinear Analysis: Real World Applications, 6 (2005) 563-587. doi: 10.1016/j.nonrwa.2004.12.012
   Web of Science ®Google Scholar