On a ridge high above the Golan plateau, the telltale antennae and golfball radomes of an Israeli surveillance station point north-east towards Damascus. In the valley below, minefields, barbed wire fences and a blue UN flag mark the frontline between the two most powerful armies in the Middle East. Behind it is a country in the throes of civil war.

Round the clock, from its perch on Mount Avital, the Israeli army's unit 8200 eavesdrops on Syria, a former bastion of stability that is now crumbling along with other old certainties about the region. It is simple enough, say, to monitor the communications of an armoured division or track a MiG fighter squadron, but far harder to understand the calculations going on in Bashar al-Assad's head. "Tanks are the easiest thing to follow," says a veteran intelligence officer in Tel Aviv.

Ora Peretz lives in a kibbutz founded when Israel conquered the Golan Heights in 1967 and runs a cafe selling cherries, coffee and cold drinks. "We see terrible things on TV about what is happening in Syria," she said, as a group of tourists peered across no-man's land at the ruins of Quneitra. "But it's quiet here. People say Assad might try to do something desperate. But I know we are ready if he does."

The potential fallout from a disintegrating Syria is not Israel's only worry. Last month's election victory for the Muslim Brotherhood's Mohamed Morsi in Egypt and jitters about unrest in Jordan have raised troubling questions about the country's peace treaties with two of its immediate neighbours. In Lebanon, the third neighbour, Hezbollah – armed by Iran and Syria – is seen as a permanent challenge to Israel's regional dominance. Israel's once close relations with Turkey are in ruins.

Official discourse in Israel frowns on the romantic phrase "the Arab spring". The reference point is more Tehran 1979 than Berlin 1989. In government offices the preferred terms are "awakening" or plain "unrest".

Politicians do use a seasonal metaphor, but a far chillier one. "For us it is an Islamist winter," says Ronnie Bar-On, chairman of the Knesset foreign affairs and defence committee. A colour photograph of Auschwitz above his desk is a bleak reminder of what still makes many Israelis tick.

Binyamin Netanyahu, the Likud prime minister, likes to describe the Middle East as a "tough neighbourhood". Ehud Barak, his defence minister, once compared Israel to a "villa in the jungle" – a phrase that smacked of colonialism and racism. In recent months both have warned of the danger of Iran going nuclear and hinted at a pre-emptive attack to stop it – and maintain Israel's atomic supremacy. But developments closer to home are deeply unsettling. Israel's relations with the Arab world and its strategic position in the Middle East have reached "a new low", in the words of Itamar Rabinovich, a leading historian of the Middle East and a former ambassador to the US.

In Israel's foreign and defence ministries, officials admit they were taken by surprise by events. Distant Tunisia had been of little interest since Yasser Arafat brought the PLO back from there to Gaza and the West Bank in the wake of the Oslo agreement in 1993. Libya is remote, too. Egypt, the largest Arab state and the first to break ranks and make peace with Israel, is another story. "When Mubarak fell the Arab world was stunned and we were as well," says a senior official in Jerusalem.

Last year, as the world watched the drama of Tahrir Square, Binyamin Ben-Eliezer, a one-time Labor defence minister, deplored the overthrow of Mubarak and even offered him asylum in Israel. It was proof for Egyptians enraged by their president's complicity in the Gaza blockade and his silence during the 2009 "Cast Lead" war that the old regime was on the "wrong" side of history.

Nervous reactions duly followed. In September, after five Egyptian policemen were killed by Israeli troops pursuing Palestinian gunmen in Sinai, a crowd stormed Israel's embassy in Cairo and its terrified staff had to be evacuated. "Darkness falls on Egypt," screamed one Hebrew paper, echoing the biblical 10 plagues, when Morsi beat Mubarak's former prime minister Ahmed Shafiq to the presidency.

Publicly, the government response has been low-key. In private Israel fears that in the longer term the Islamists will strengthen their position in relation to the Supreme Council of the Armed Forces. For now, Israel's links with the Egyptian military and mukhabarat security people are still functioning well. No one expects the 1979 peace treaty to be scrapped, if only because it would risk $1.3bn in annual defence support from the US, though there may well be an attempt to renegotiate its military provisions. Egyptian public opinion will now be far harder to ignore.

Other problems loom. There is concern about the Sinai peninsula where, the Israelis say, extremist Salafi groups are operating. Attacks on gas pipelines have become routine, as has weapon-smuggling from Sudan and Libya to Hamas and Islamic Jihad in Gaza. For Israel's armed Palestinian enemies, the lawless desert provides useful depth. "When we looked at our overall threat assessment of the region three years ago, Egypt was barely mentioned," recalls the senior official. "It's not a threat now, but there are a lot of question marks."

To the east, Jordan is a new source of anxiety. Its 1994 peace treaty with Israel is vital to the western-backed monarchy but has always been unpopular. Over the last turbulent year King Abdullah has faced more problems with the traditionally loyal East Bank tribes than from the restive Palestinians.

If Assad falls, tensions are likely to rise in Jordan and its Muslim Brotherhood will be emboldened. That treaty is also safe for now, according to Meir Dagan, the last head of the Mossad and guardian of the special relationship with Amman. Avigdor Lieberman, Netanyahu's super-hawkish foreign minister, has gone out of his way to reassure Jordan there is no truth to rumours that Israel is scheming to turn it into an "alternative homeland" for the Palestinians so it can keep hold of the West Bank for good.

If all this adds up to an alarming picture, the dangers are different from in the past, say the experts. "In the 1950s and 1960s we Israelis worried about Arab power – that we might be overwhelmed by them and their Soviet weapons," says Asher Susser of Tel Aviv University. "Now we face the fallout of Arab weakness."

Last May, for example, on "Nakba" day – commemorating the loss of Palestine in 1948 – hundreds of Palestinians marched across the normally strictly controlled Golan border from Quneitra right under the antennae on Mount Avital. It was the first time it had been breached in three decades, a handy diversion for a beleaguered Assad. The possible leakage or theft of Syrian chemical weapons or the emergence of al-Qaida-type terrorism are other headaches.

In the defence establishment there is recognition that Israel's traditional interest in regime stability and the military has been too narrow; that understanding the novelty of Arab "people power" requires a shift in focus. "When the regimes around us were dictatorships to a greater or lesser degree, most of what IDF [Israel Defence Forces] intelligence and Mossad researchers had to do was to focus on the man at the top of the pyramid and the small group of generals, advisers and relatives under him," wrote Amos Harel, military correspondent of the liberal daily Ha'aretz. "Tahrir Square changed all that. Suddenly the intelligence services are talking about whole nations, public opinion and social networks."

Menachem Klein, a political scientist at Bar Ilan University, believes the Arab spring has pushed Israel deeper into a defensive "bunker mentality" in the face of events it perceives as existential threats rather than as circumstances that have been created partly by itself, especially by continuing to build illegal settlements in the West Bank and East Jerusalem.

For 12 years, since the collapse of the Camp David talks and the second intifada, there has been an impasse on the issue at the heart of the Arab-Israeli conflict. Netanyahu's government says it would refuse to negotiate with a Palestinian unity government which includes the Islamists of Hamas, who refuse to abandon armed resistance or formally recognise the Jewish state. The PLO is adamant that it will not talk while settlement activity goes on. The two-state solution to the conflict thus looks less and less likely to be achieved.

Mahmoud Abbas's Palestinian Authority, created under Oslo as a temporary administration, still rules in Ramallah but it has not been immune to the winds of change.

Strapped for cash and co-operating closely on security with Israel – enemies accuse the PLO leader of "collaboration" – it, too, faces dissent at home. "It would be a mistake to leave the Palestinians out of the picture of the Arab spring," says Klein. "Israel's nightmare is that Abbas collapses and Hamas takes over. I wouldn't be surprised if he fell. We didn't think that Assad or Mubarak would lose power either."

No one expects a revived peace process any time soon. "For the foreseeable future," predicts Shlomo Avineri, former director-general of the foreign ministry, "regardless of what is happening around the region there are not going to be any meaningful Israeli-Palestinian negotiations." The best hope, say western diplomats, is "muddling through" until after the US presidential election in November, and hope that no new intifada erupts.

Part of the price of this long impasse is the fading of the 2002 Arab peace initiative, in which all 21 Arab states – remarkably in the light of the history of the conflict – offered full recognition of Israel in return for a just settlement of the Palestinian issue. "The Arab initiative is not really relevant any more," warns Gilad Sher, a former Israeli negotiator. "No Israeli government ever found it interesting enough to even discuss it. That's a pity. And now we don't know who will be sitting in the room. Who will represent Syria, Libya? Who are the representatives of the Palestinians – the PLO or Hamas?"

Many Israeli Jews seem largely indifferent to all this. "The Arab spring is a non-story here," suggests Tom Segev, a historian and columnist. "Most people think things can go on for ever. Bibi [Netanyahu] has managed to create the impression that there's no Palestinian partner for peace and that everything is just fine. Israelis tend not to be interested in Arabs as people but as enemies. Sure, people will be pleased when Assad falls, as we were when Saddam went. But it won't make any difference to the cost of renting an apartment in Tel Aviv."

For some, surveying these historic changes in the region, the lesson is obvious. "In the 1950s and 1960s the message from the Arab world to Israel was clear: 'We hate you and we don't want you here,' " says Tel Aviv university professor Eyal Zisser, Assad's biographer. "Now the message is: 'We hate you and we don't want you here but you are here and what can we do about it?' It's not a love story but it is a sort of acceptance and that is important, and Israel should not ignore it. Israel should do something in response and that has to mean movement on the Palestinian question. What makes an Egyptian Arab or a Tunisian Arab? It's the Palestinian question. Israel needs to send a positive message on this to the Arab masses."

Optimists see opportunities as well as threats. Assad's fall would be a serious blow to Iran and to Hezbollah, gains that outweigh the old "better the devil you know" argument about stability in Damascus and quiet on the Golan.

From Cairo, Morsi might influence Hamas – a branch of the Muslim Brotherhood – to moderate its position on Israel, if the restrictions on Gaza are significantly eased. Turmoil, however, looks more likely to breed caution than risk-taking in the current climate. "There is a benign scenario about Egypt," agrees a Netanyahu aide, "but not many of our national security people believe in it."

In his Knesset office, Ronnie Bar-On sums up the view from Jerusalem. "The picture is definitely grim. It's true that change can be an opportunity, but for the moment I don't hear the bells ringing."