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[[File:VanDerPolOscillator.png|thumb|[[Phase portrait]] of the unforced Van der Pol oscillator, showing a [[limit cycle]] and the [[direction field]].]]
To make the tax system more progressive, the Government is elevating property tax rates for top-end residential properties in Singapore Finances 2013, with the largest increases making use of to funding properties that are not occupied by their owners.<br><br>a) The utmost strata ground space of new EC models will likely be capped at a hundred and sixty sq. metres. b) Sales of latest dual-key EC units might be restricted to multi-generational households solely. Loans exceeding 30 years tenure will face considerably tighter mortgage-to-worth (LTV) limits. This may apply to both personal properties and HDB flats. [http://www.kiddiewink.org/groups/guide-to-new-singapore-property-gross-sales-launches/ New Ec Launch Singapore] rules on loan tenure A concession to defer Stamp Responsibility cost on all contracts was introduced in June 1998 as part of the off-funds measures to cushion the impact of financial slowdown. The Government has decided to withdraw the concession with rapid impact (from 15 December 2006) as the financial circumstances and the property market have improved. A) Progressive tax charges for non-owner occupied properties Dog Will get Helps For House Hearth<br><br>In any given market across the country, one in all these market outcomes might be in play already. Real property is native, and those excessive dollar homes along the coast in California could lock up their owners with golden handcuffs. Nonetheless, go to a small town in the South or Midwest, and you could possibly see the exodus of retirees creating a surge in housing inventory. The good news is that real property investors are prepared for either situation, and there's revenue in being ready. I'm excited and searching forward to the opportunities either or both of these conditions will provide; thanks Boomers! The Citron Residences is a singular blended residential and business development situated at 1 Marne Street in prime District 08. A mere stone\'s throw aw  Learn More<br><br>Some previous-school physicians nonetheless suppose that drugs are the one method to make us wholesome. What concerning the unintended effects? Wouldn't it make more sense to scrub up somebody's life-style first and if the health difficulty persists, then think about drugs? You'll think it's common sense, however perhaps to not all. If you can't already tell, this can be a matter I am very captivated with. There's a recent New England Journal of Medication article that helps us all - including the skeptics about lifestyle adjustments - to see that lifestyle changes are in reality beneficial for our well being. To say that a nutritious diet and train life-style is unimportant is totally ludicrous once we as health care practitioners have the job of instituting health measures for our patients.<br><br>An undercover investigation led by the BBC found " surprising quantities" of "probably unsafe" rat meat bought at one in all London's most popular markets, Ridley Highway Market. Large portions of other illegal bushmeat had been additionally for sale. We are a group of property advisor specialist, concentrate on selecting the need dwelling for our purchasers. Having stated that, we now have help our purchasers to efficiently choose their very own need house again and again. Woodlands EC Forestville @ Woodlands The simplest means is to contact an actual property agent who is a Advertising and marketing Team Member The agent will likely meet to show you particulars of the project provided by the developer. Your cheque might be returned to you in the event you resolve to not proceed to purchase. You aren't obliged to proceed to buy.<br><br>Subsequent yr there will be quite a no. of new venture launches that can sooth the market. Whether to purchase now or later will also is dependent upon which undertaking / district you are taking a look at and the transactions going on for that area. Bartley Ridge is the most popular new launch in district thirteen. Irresistible pricing from $1,1xx psf. Bartley Ridge is a 99-yr leasehold new condo at Mount Vernon highway, good next to Bartley MRT station (CC12). If you want to get extra a) borrow up to 50% of property value in the event you should not have an present housing loan a) borrow as much as 60% of property worth if you don't have an current housing mortgage b) borrow as much as 40% of property worth if you have an existing housing mortgage Tuas South Street 5 Industrial Web site on the market District 13, Freehold condominium<br><br>This revised property tax construction will be phased in over two years, from Jan 1, 2014. Foreigners and non-people (company entities) buying any residential property can pay an ABSD ( Extra Purchaser's Stamp Obligation ) of 10%; Permanent Residents (PRs) proudly owning one and shopping for the second and subsequent residential property can pay an ABSD ( Extra Purchaser's Stamp Obligation ) of 3%; and Lower the Mortgage-To-Value (LTV) limit to 50% on housing loans granted by monetary establishments regulated by MAS for property purchasers who will not be individuals1; and Sold inside the second year of purchase, i.e. the property is held for greater than 1 yr and as much as 2 years – 2/three of the complete SSD fee. For more data on property tax, please seek advice from IRAS' web site.
[[File:VanderPol-lc.svg|thumb|Evolution of the limit cycle in the phase plane. Notice the limit cycle begins as circle and, with varying ''&mu;'', become increasingly sharp. An example of a [[Relaxation oscillator]].]]
In [[dynamical system|dynamics]], the '''Van der Pol oscillator''' is a [[Conservative force|non-conservative]] [[oscillator]] with [[nonlinearity|non-linear]] [[damping]].  It evolves in time according to the second order [[differential equation]]:
 
:<math>{d^2x \over dt^2}-\mu(1-x^2){dx \over dt}+x= 0</math>
 
where ''x'' is the position [[coordinate system|coordinate]] &mdash; which is a [[function (mathematics)|function]] of the time ''t'', and ''&mu;'' is a [[scalar (mathematics)|scalar]] parameter indicating the nonlinearity and the strength of the damping.
 
==History==
The Van der Pol oscillator was originally proposed by the Dutch [[electrical engineering|electrical engineer]] and physicist [[Balthasar van der Pol]] while he was working at [[Philips]].<ref name="Biography">Cartwright, M.L., [http://jlms.oxfordjournals.org/cgi/pdf_extract/s1-35/3/367 "Balthazar van der Pol"], [[Journal of the London Mathematical Society|''J. London Math. Soc.'']], '''35''', 367-376, (1960).</ref> Van der Pol found stable oscillations, which he called [[relaxation oscillator|relaxation-oscillations]]<ref name="relax">Van der Pol, B., "On relaxation-oscillations", [[Philosophical Magazine|''The London, Edinburgh and Dublin Phil. Mag. & J. of Sci.'']], '''2'''(7), 978-992 (1927).</ref> and are now known as [[limit cycle]]s, in [[electrical circuit]]s employing [[vacuum tube]]s. When these circuits were driven near the limit cycle they become [[entrainment (physics)|entrained]], i.e. the driving [[signal (electrical engineering)|signal]] pulls the current along with it. Van der Pol and his colleague, van der Mark, reported in the September 1927 issue of [[Nature (journal)|Nature]] <ref name="Nature">Van der Pol, B. and Van der Mark, J., “Frequency demultiplication”, ''Nature'', '''120''', 363-364, (1927).</ref> that at certain drive [[frequency|frequencies]] an irregular [[noise (electronic)|noise]] was heard. This irregular noise was always heard near the natural entrainment frequencies. This was one of the first discovered instances of [[chaos theory|deterministic chaos]].<ref>Kanamaru, T., [http://www.scholarpedia.org/article/Van_der_Pol_oscillator "Van der Pol oscillator"], ''[[Scholarpedia]]'', '''2'''(1), 2202, (2007).</ref>
 
The Van der Pol equation has a long history of being used in both the [[physical science|physical]] and [[biology|biological]] [[science]]s. For instance, in biology, Fitzhugh<ref name="fitz">FitzHugh, R., “Impulses and physiological states in theoretical models of nerve membranes”, ''[[Biophysical Journal|Biophysics J]]'', '''1''', 445-466, (1961).</ref> and Nagumo<ref name="nag">Nagumo, J., Arimoto, S. and Yoshizawa, S. "An active pulse transmission line simulating nerve axon", ''[[Proc. IRE]]'', '''50''', 2061-2070, (1962).</ref> extended the equation in a [[plane (mathematics)|planar field]] as a [[FitzHugh–Nagumo model|model]] for [[action potential]]s of [[neurons]]. The equation has also been utilised in [[seismology]] to model the two plates in a [[geological fault]].<ref>Cartwright, J., Eguiluz, V., Hernandez-Garcia, E. and Piro, O., "Dynamics of elastic excitable media", [[International Journal of Bifurcation and Chaos|''Internat. J. Bifur. Chaos Appl. Sci. Engrg.'']], '''9''', 2197–2202, (1999).</ref>
 
== Two dimensional form ==
[[Liénard's Theorem]] can be used to prove that the system has a limit cycle. Applying the Liénard transformation <math>y = x - x^3/3 - \dot x/\mu</math>, where the dot indicates the time derivative, the Van der Pol oscillator can be written in its two-dimensional form:<ref>Kaplan, D. and Glass, L., ''Understanding Nonlinear Dynamics'', Springer, 240-244, (1995).</ref>
:<math>\dot x = \mu \left(x-\frac{1}{3}x^3-y\right)</math>
:<math>\dot y = \frac{1}{\mu} x.</math>
Another commonly used form based on the transformation <math>y = \dot x </math> is leading to
:<math>\dot x = y</math>
:<math>\dot y = \mu(1-x^2) y-x.</math>
 
==Results for the unforced oscillator==
[[File:Vanderpol mu=5.svg|thumb|right|[[Relaxation oscillation]] in the Van der Pol oscillator without external forcing. The nonlinear damping parameter is equal to ''μ''&nbsp;=&nbsp;5.]]
Two interesting regimes for the characteristics of the unforced oscillator are:<ref>Grimshaw, R., ''Nonlinear ordinary differential equations'', [[CRC Press]], 153–163, (1993), ISBN 0-8493-8607-1.</ref>
 
*When ''&mu;'' = 0, i.e. there is no damping function, the equation becomes:
 
::<math>{d^2x \over dt^2}+x= 0.</math>
 
:This is a form of the [[harmonic oscillator|simple harmonic oscillator]] and there is always [[conservation of energy]].
 
*When ''&mu;'' > 0, the system will enter a limit cycle. Near the origin ''x''&nbsp;=&nbsp;''dx''/''dt''&nbsp;=&nbsp;0 the system is unstable, and far from the origin the system is damped.
 
==The forced Van der Pol oscillator==
[[File:Vanderpol time mu=8.53 A=1.2 T=10.svg|thumb|right|[[Chaos theory|Chaotic behaviour]] in the Van der Pol oscillator with sinusoidal forcing. The nonlinear damping parameter is equal to ''μ''&nbsp;=&nbsp;8.53, while the forcing has amplitude ''A''&nbsp;=&nbsp;1.2 and angular frequency ''ω''&nbsp;=&nbsp;2π&nbsp;/&nbsp;10.]]
The forced, or driven, Van der Pol oscillator takes the 'original' function and adds a driving function ''A''sin(''&omega;t'') to give a differential equation of the form:
 
:<math>{d^2x \over dt^2}-\mu(1-x^2){dx \over dt}+x-A \sin(\omega t)= 0,</math>
 
where ''A'' is the [[amplitude]], or [[Displacement (vector)|displacement]], of the [[wave equation|wave function]] and ''&omega;'' is its [[angular velocity]].
 
==Popular culture==
[[File:Van der pol triode.svg|thumb|right|[[Electrical circuit]] involving a [[triode]], resulting in a forced Van der Pol oscillator.<ref name=Tomita>K. Tomita (1986): "Periodically forced nonlinear oscillators". In: ''Chaos'', Ed. Arun V. Holden. Manchester University Press, ISBN 0719018110, pp. 213–214.</ref>  The circuit contains: a triode, a [[resistor]] ''R'', a [[capacitor]] ''C'', a coupled [[inductor]]-set with [[self inductance]] ''L'' and [[mutual inductance]] ''M''.  In the serial [[RLC circuit]] there is a current ''i'', and towards the triode [[anode]] ("plate") a current ''i<sub>a</sub>'', while there is a voltage ''u<sub>g</sub>'' on the triode [[control grid]]. The Van der Pol oscillator is forced by an AC [[voltage source]] ''E<sub>s</sub>''.]]
Author [[James Gleick]] described a vacuum-tube Van der Pol oscillator in his book [[Chaos: Making a New Science]].<ref name=gleick-chaos>{{cite book|last=Gleick|first=James|title=Chaos: Making a New Science|year=1987|publisher=Penguin Books|location=New York|isbn=0-14-009250-1|pages=41–43}}</ref>  According to a [[New York Times]] article,<ref name=colman-nyt>{{cite news|last=Colman|first=David|title=There's No Quiet Without Noise|url=http://www.nytimes.com/2011/07/10/fashion/a-machine-designed-to-add-chaos-to-order.html|accessdate=11 July 2011|newspaper=New York Times|date=11 July 2011}}</ref> Gleick received a modern electronic Van der Pol oscillator from a reader in 1988.
 
== See also ==
* [[Mary Cartwright]], British mathematician, one of the first to study the theory of deterministic chaos, particularly as applied to this oscillator.
 
==References==
{{reflist}}
 
==External links==
* {{springer|title=Van der Pol equation|id=p/v096030}}
* [http://scholarpedia.org/article/Van_der_Pol_oscillator Van der Pol oscillator on Scholarpedia]
* [http://www.cmp.caltech.edu/~mcc/Chaos_Course/Lesson3/Demos.html Van Der Pol Oscillator Interactive Demonstrations]
* [http://www.nytimes.com/2011/07/10/fashion/a-machine-designed-to-add-chaos-to-order.html There's No Quiet Without Noise, New York Times]
 
{{Chaos theory}}
 
[[Category:Chaotic maps]]
[[Category:Dutch inventions]]
[[Category:Ordinary differential equations]]

Latest revision as of 17:56, 3 November 2014

To make the tax system more progressive, the Government is elevating property tax rates for top-end residential properties in Singapore Finances 2013, with the largest increases making use of to funding properties that are not occupied by their owners.

a) The utmost strata ground space of new EC models will likely be capped at a hundred and sixty sq. metres. b) Sales of latest dual-key EC units might be restricted to multi-generational households solely. Loans exceeding 30 years tenure will face considerably tighter mortgage-to-worth (LTV) limits. This may apply to both personal properties and HDB flats. New Ec Launch Singapore rules on loan tenure A concession to defer Stamp Responsibility cost on all contracts was introduced in June 1998 as part of the off-funds measures to cushion the impact of financial slowdown. The Government has decided to withdraw the concession with rapid impact (from 15 December 2006) as the financial circumstances and the property market have improved. A) Progressive tax charges for non-owner occupied properties Dog Will get Helps For House Hearth

In any given market across the country, one in all these market outcomes might be in play already. Real property is native, and those excessive dollar homes along the coast in California could lock up their owners with golden handcuffs. Nonetheless, go to a small town in the South or Midwest, and you could possibly see the exodus of retirees creating a surge in housing inventory. The good news is that real property investors are prepared for either situation, and there's revenue in being ready. I'm excited and searching forward to the opportunities either or both of these conditions will provide; thanks Boomers! The Citron Residences is a singular blended residential and business development situated at 1 Marne Street in prime District 08. A mere stone\'s throw aw Learn More

Some previous-school physicians nonetheless suppose that drugs are the one method to make us wholesome. What concerning the unintended effects? Wouldn't it make more sense to scrub up somebody's life-style first and if the health difficulty persists, then think about drugs? You'll think it's common sense, however perhaps to not all. If you can't already tell, this can be a matter I am very captivated with. There's a recent New England Journal of Medication article that helps us all - including the skeptics about lifestyle adjustments - to see that lifestyle changes are in reality beneficial for our well being. To say that a nutritious diet and train life-style is unimportant is totally ludicrous once we as health care practitioners have the job of instituting health measures for our patients.

An undercover investigation led by the BBC found " surprising quantities" of "probably unsafe" rat meat bought at one in all London's most popular markets, Ridley Highway Market. Large portions of other illegal bushmeat had been additionally for sale. We are a group of property advisor specialist, concentrate on selecting the need dwelling for our purchasers. Having stated that, we now have help our purchasers to efficiently choose their very own need house again and again. Woodlands EC Forestville @ Woodlands The simplest means is to contact an actual property agent who is a Advertising and marketing Team Member The agent will likely meet to show you particulars of the project provided by the developer. Your cheque might be returned to you in the event you resolve to not proceed to purchase. You aren't obliged to proceed to buy.

Subsequent yr there will be quite a no. of new venture launches that can sooth the market. Whether to purchase now or later will also is dependent upon which undertaking / district you are taking a look at and the transactions going on for that area. Bartley Ridge is the most popular new launch in district thirteen. Irresistible pricing from $1,1xx psf. Bartley Ridge is a 99-yr leasehold new condo at Mount Vernon highway, good next to Bartley MRT station (CC12). If you want to get extra a) borrow up to 50% of property value in the event you should not have an present housing loan a) borrow as much as 60% of property worth if you don't have an current housing mortgage b) borrow as much as 40% of property worth if you have an existing housing mortgage Tuas South Street 5 Industrial Web site on the market District 13, Freehold condominium

This revised property tax construction will be phased in over two years, from Jan 1, 2014. Foreigners and non-people (company entities) buying any residential property can pay an ABSD ( Extra Purchaser's Stamp Obligation ) of 10%; Permanent Residents (PRs) proudly owning one and shopping for the second and subsequent residential property can pay an ABSD ( Extra Purchaser's Stamp Obligation ) of 3%; and Lower the Mortgage-To-Value (LTV) limit to 50% on housing loans granted by monetary establishments regulated by MAS for property purchasers who will not be individuals1; and Sold inside the second year of purchase, i.e. the property is held for greater than 1 yr and as much as 2 years – 2/three of the complete SSD fee. For more data on property tax, please seek advice from IRAS' web site.

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