By Stancho Dimiev, Kouei Sekigawa
ISBN-10: 9812707905
ISBN-13: 9789812707901
This quantity includes the contributions via the contributors within the 8 of a sequence workshops in advanced research, differential geometry and mathematical physics and comparable components. lively experts in mathematical physics give a contribution to the quantity, offering not just major info for researchers within the zone but additionally attention-grabbing arithmetic for non-specialists and a broader viewers. The contributions deal with subject matters together with differential geometry, partial differential equations, integrable structures and mathematical physics.
Read Online or Download Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics: Proceedings of the 8th International Workshop on Complex Structures ... and Infomatics, Bulgaria, 21-26 August PDF
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Extra resources for Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics: Proceedings of the 8th International Workshop on Complex Structures ... and Infomatics, Bulgaria, 21-26 August
Sample text
250000000. Hence the field lines of the originar system are linear unstable, and the extended system is Jacobi unstable. The Jacobi stability depends on the variation of the parameters. We shall discuss further the impact of the change of the parameters γ and θ on the structural behavior of the extended SODE (3)–(4). Considering the parameter θ variable within the interval (0,1) with γ fixed, we get the following results regarding the linear and the Jacobi stability. 2. Let γ = 4 (the limit cycle value).
It was proved that for γ = 4, one obtains a limit cycle and that the SODE exhibits a Hopf bifurcation; it provides a model with negative feedback (inhibition) as shown in the following diagram excitation excitation inhibition x1 −−−−−−−→ x2 −−−−−−−→ x3 −−−−−−−→ x1 . 0. In practice are used iterated pulses with initial value z0 and zn = δ(e−nτ /tc − 1) z0 e−nτ /tc + . Then the asymptotic value (for n → ∞) is 1 − eτ /tc z∞ = δ/(eτ /tc − 1). The response γ or γ0 and the time constant tc are refered as network parameters — which are inherent properties of the network, and δ and τ are referred as stimulation parameters — which are the stimulation pulse amplitude and stimulation period, respectively.
Chern, Sur la geometrie d’un syst`eme d’equations differentialles du second ordre, Bull. Sci. Mat. 63 (1939), 206–212. 9. D. Kosambi, Parallelism and path space, Math. Zeitschrift 37 (1933), 608– 618. 10. R. Nicola and V. Balan, Jacobi stability for dynamical systems with applications to biology, Proc. of the 3-rd International Colloquium “Mathematics in Engineering and Numerical Physics” (MENP-3), 7–9 October 2004, Bucharest, Romania, BSG Proceedings 12, Geometry Balkan Press, Bucharest, 195–201.
Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics: Proceedings of the 8th International Workshop on Complex Structures ... and Infomatics, Bulgaria, 21-26 August by Stancho Dimiev, Kouei Sekigawa
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